Satyanad Kichenassamy
Professeur des Universités
Laboratoire de Mathématiques de Reims (CNRS UMR9008)
Université de Reims Champagne-Ardenne
Moulin de la Housse - B.P. 1039
F-51687 Reims Cedex 2
France
My e-mail address follows the general format: firstname.lastname@univ-reims.fr
Ph.: +33(0)3.26.91.83.89

https://orcid.org/0000-0002-9767-4938

• Tamoul/Tamil: சத்தியநாத் கிஷ்ணசாமி (or கிருஷ்ணஸ்வாமி )
• Devanāgarī (Sanskrit): सत्यनाद् किष्णसामि (or कृष्णस्वामि)
• Russe/Russian: Сатйана́д Кишнасса́ми

• Ancien élève de l'Ecole Normale Supérieure (rue d'Ulm, 1982-1986).
• Agrégation (Mathématiques, 1984).
• Thèse: Problèmes Quasilinéaires Elliptiques,
  Doctorat de Mathématiques, Université Paris VI, soutenue le 26 janvier 1987/defended January 26, 1987
  (directeur/advisor: Haïm Brezis).
• Habilitation à diriger des recherches en sciences (5 février 1998; Paris VII).
• Depuis/Since sept. 1998: Professeur des Universités, Université de Reims Champagne-Ardenne.
• 2004-2007: Directeur du Laboratoire de Mathématiques de Reims (CNRS, UMR 6056).
• 2021-2022: Chargé de conférences à l'EPHE (Université PSL (Paris Sciences & Lettres)) : L'histoire et l'historiographie des Mathématiques en Inde : Le discours apodictique dans les sources sanskrites. / History and Historiography of Mathematics in India : Apodictic discourse in Sanskrit sources Les séances en présentiel auront lieu à l'EPHE (22 et 29 octobre 2021, 4, 19 et 26 novembre 2021, 10 décembre 2021) et les séances en mode hybride à la Sorbonne (14, 21 et 28 janvier 2022, 4, 11, 18 et 25 février 2022). (Hybrid mode, in French and English.)

Analyse Non Linéaire ; Géométrie Différentielle; Relativité ; Vision par Ordinateur ; Histoire des Mathématiques; Indianisme.

Nonlinear Analysis; Differential Geometry; Relativity; Computer Vision; History of Mathematics; Indology.

Membre de la / Member of the Société asiatique, de la / of the Société Mathématique de France, et de l' / and of the American Mathematical Society.

• Axioms (2021-).
• International Journal of Analysis and Applications (as Advisory Editor, 2017-).
• Abstract and Applied Analysis (2011-2019).
• International Mathematical Forum (formerly: International Mathematical Journal) (2002-2014).

• Publié chez/Source: Marcel Dekker, New York, September 1995. (ISBN-10: 8247-9328-5, ISBN-13: 978-0824793289)
• Préface.
• Table des matières/Table of contents.
• Reviews

• Publié chez/Source: Birkhäuser, Boston, October 2007. (ISBN: 978-0-8176-4352-2)
• Volume 71 of the series: Progress in Nonlinear Differential Equations and Their Applications.
• Version électronique (eBook): ISBN 978-0-8176-4637-0
• Click here for content, preview and other information.
• Review (Mathematical Reviews).
• Review (Monatshefte für Mathematik (2009) 158:329-330).
• Review (Zentralblatt für Mathematik).

• Symmetric Hyperbolic Systems and Shock Waves, in Encyclopedia of Mathematical Physics, vol. 5,
  J.-P. Françoise, G. L. Naber, Tsou S. T. (eds.),
  Oxford : Elsevier, pp. 160-166 (2006) (ISBN 978-0-1251-2666-3). Link to PDF
• Schauder-type Estimates and Applications,
  Chapter 5 of the Handbook of Differential Equations, Section Stationary Partial Differential Equations, vol. 3,
  M. Chipot and P. Quittner (eds.),
  Elsevier, pp. 401-464 (2006) (ISBN 978-0-444-52846-9). Link to PDF
• L'emploi métonymique de l'arbre kallāl dans la philosophie médiévale en pays tamoul,
  L'Arbre en Asie,
  P.-S. Filliozat et M. Zink éd.,
  Académie des Inscriptions et Belles-Lettres, Paris, 2018, pp. 273-295 (ISBN : 978-2-87754-372-9).
• La légende de la colonne de lumière : une analyse indienne du problème de l'origine du monde,
  Mythes d'origine dans les civilisations de l'Asie,
  P.-S. Filliozat et M. Zink éd.,
  Académie des Inscriptions et Belles-Lettres, Paris, 2021, pp. 145-167 (ISBN : 978-2-87754-672-0).

1. Solutions Positives des Équations Quasilinéaires Elliptiques,
   C. R. Acad. Sci. Paris, 300, série 1 (1985) 589-591
   (with J. Smoller).
2. Singularités Isolées de l'Équation  div (|∇u|^(p-2)∇u)=0,
   C. R. Acad. Sci. Paris, 301, série 1 (1985) 149-151
   (with L. Véron).
3. Singular Solutions of the p-Laplace Equation,
   Math. Ann., 275 (1986) 599-615
   (with L. Véron). Link to PDF. Link to text.
4. Local Index of Potential Operators of Monotone Type,
   Houston J. of Math., 16 : 1 (1990) 139-149. Link to PDF. 0ther link to PDF.
5. Quasilinear Problems with Singularities,
   Manuscripta Math., 57 (1987) 281-313. Link to PDF, Link to text.
6. Périmètre sur les Variétés et Applications aux Équations aux Dérivées Partielles,
   Séminaire E. D. P. 1986?87, École Polytechnique, France. Link to PDF
7. Symmetrization on the Sphere and Applications,
   in Nonlinear Partial Differential Equations and Applications, Collège de France Seminar vol. X (1987-88), (H. Brezis and J.-L. Lions (Eds.), Pitman Res. Notes in Math. Series, volume 220, Longman Sci. Tech., Harlow, pp. 272-283 (1991).
8. Energy Estimates for Surface-Valued Maps with Prescribed Singularities,
   in Nonlinear Variational Problems: Volume 2, (A. Marino and M. K. V. Murthy Eds.), 1989, pp. 92-98
   (with H. Brezis).
9. Compactness Theorems for Differential Forms,
   Commun. Pure and Appl. Math., 42 (1989) 47-54. Link to PDF
10. On the Existence of Radial Solutions of Quasilinear Elliptic Equations,
    Nonlinearity, 3 (3) (August 1990) 677-694
    (with J. Smoller). Link to PDF
11. Breather Solutions of the Nonlinear Wave Equation,
    Commun. Pure and Appl. Math., 44 (1991) 789-818. Link to PDF Other link to PDF
12. Breathers and the Sine-Gordon Equation,
    Contemporary Mathematics, 122 (1991) 73-76.
13. Existence and Non-existence of Solitary Wave Solutions to Higher Order Model Evolution Equations,
    SIAM J. Math. Anal., 23 (5) (Sept.1992) 1141-1166
    (with P. J. Olver). Link to PDF
14. Blow-up Surfaces for Nonlinear Wave Equations, Part I,
    Commun. in P. D. E., 18(3&4) (1993) 431-452
    (with W. Littman). Link to PDF Other link to PDF
15. Blow-up Surfaces for Nonlinear Wave Equations, Part II,
    Commun. in P. D. E., 18(11) (1993) 1869-1899
    (with W. Littman). Link to PDF Other link to PDF
16. The Prolongation Formula for Tensor Fields,
    J. of Phys. A: Math. Gen., 27(23) (Dec. 7, 1994) 7857-7874. Link to PDF
17. Gradient Flows and Geometric Active Contour Models,
    in Proceedings of the ICCV 1995 (International Conference on Computer Vision) pp. 810-815
    (with A. Kumar, P. J. Olver, A. Tannenbaum and A. Yezzi). Link to PDF
18. The Structure of WTC Exapnsions and Applications,
    J. Phys. A: Math. Gen., 28 (7) (April 7, 1995) 1977-2004
    (with G. K. Srinivasan). Link to PDF
19. Active Contours for Visual Tracking: A Geometric Gradient Based Approach,
    in Proceedings of the 34th IEEE Conference on Decision and Control (1995), vol. 4, pp. 4041-4046
    (with A. Kumar, P. J. Olver, A. Tannenbaum and A. Yezzi). Link to PDF
20. Fuchsian Equations in Sobolev spaces and Blow-up,
    J. Differ. Eq., 125 (1996) 299-327. Link to PDF
21. Applications of the Division Theorem in H ^s,
    J. of Dynamics and Differ. Eq., 8 (3) (1996) 407-425. Link to PDF. Link to text.
22. The Blow-up Problem for Exponential Nonlinearities,
    Commun. in PDE, 21 (1&2) (1996) 125-162. Link to PDF Other link to PDF
23. Conformal Curvature Flows: From Phase Transitions to Active Vision,
    Archive for Rational Mechanics and Analysis, 134 (1996) 275-301
    (with A. Kumar, P. J. Olver, A. Tannenbaum and A. Yezzi). Link to PDF
24. Nonlinear Diffusion and Hyperbolic Smoothing for Edge Enhancement,
    Lect. Notes in Control and Info. Sci., 219, Springer Verlag, Berlin, pp. 119-124 (1996). Link to PDF
25. A Geometric Snake Model for Segmentation of Medical Imagery,
    IEEE Transactions on Medical Imaging, 16 (2) (April 1997) 199-209
    (with A. Kumar, P. J. Olver, A. Tannenbaum and A. Yezzi). Link to PDF
26. The Perona-Malik Paradox,
    SIAM Journal of Applied Mathematics, 57 (5) (October 1997) 1328-1342. Link to PDF
27. Existence of Solitary Waves for Water-wave Models,
    Nonlinearity, 10 (1) (January 1997) 133-151. Link to PDF
28. Instability of Pole Singularities for the Chazy Equation,
    J. Phys. A: Math. Gen., 31 (11) (1998) 2675-2690. Link to PDF
29. Analytic Description of Singularities in Gowdy Spacetimes,
    Classical and Quantum Gravity, 15 (5) (1998) 1339-1355.
    (with A. D. Rendall). Link to PDF
30. WTC Expansions and Non-integrable Equations,
    Studies in Applied Mathematics, 102 (1999) 1-26. Link to PDF
31. Asymptotic Behavior in Polarized T²-symmetric Spacetimes,
    Journal of Mathematical Physics, 40 (1) (January 1999) 340-352
    (with J. Isenberg). Link to PDF
32. Stability of Blow-up Patterns for Nonlinear Wave Equations,
    Contemporary Mathematics, 255 (2000) 139-162.
33. Explosion et Normes L ^p pour l'équation des Ondes Nonlinéaire Cubique,
    C. R. Acad. Sci. Paris, sér I, 355 (11) (2002) 903-908
    (with G. Cabart). Link to PDF
34. A Linear Fuchsian Equation with Variable Indices,
    J. Differ. Eq., 190 (1) (2003) 64-80
    (with A. Bentrad). Link to PDF
35. Stellar Models and Irregular Singularities,
    Communications in Contemporary Mathematics, 5 (5) (2003) 719-735
    (with L. Jager). Link to PDF
36. On a Conjecture of Fefferman and Graham,
    Advances in Mathematics, 184 (2) (2004) 268-288. Link to PDF
37. Régularité du Rayon Hyperbolique,
    C. R. Acad. Sci. Paris, sér I, 338 (1) (2004) 13-18. Link to PDF
38. Boundary Blow-up and Degenerate Equations,
    Journal of Functional Analysis, 215 (2) (2004) 271-289. Link to PDF
39. La Compréhension Interlinguisitique en Inde,
    in Proceedings of the international conference organized by CIRLEP on ``L'avenir du Patrimoine Linguistique Européen,'' (The Future of Europe's Linguistic Heritage) Reims, (July 3, 2003) (E. Castagne and J.-E. Tyvaert Eds.) pp. 45-49 (2004). Link to PDF
40. Boundary Behavior in the Loewner-Nirenberg Problem,
    Journal of Functional Analysis, 222 (1) (2005) 98-113. Link to PDF
41. Recent Progress on Boundary Blow-up,
    in Elliptic and Parabolic Problems : A Special Tribute to the Work of Haïm Brezis (C. Bandle et al. eds.),
    Progress in Nonlinear Differential Equations and Their Applications, vol. 63, Birkhäuser, pp. 289-301 (2005). Link to PDF
42. Baudhāyana's rule for the Quadrature of the Circle,
    Historia Mathematica, 33 (2) (2006) 149-183. Link to PDF
43. Renormalized Variational Principles and Hardy-type Inequalities,
    Differential and Integral Equations, 19 (4) (2006) 437-448. Link
44. The Mathematical Analysis of the Perona-Malik Equation and its Practical Impact,
    Proceedings of Mathematics and Image Analysis 2006 (Paris, Sept. 18-21, 2006).
45. Théorie des Semi-groupes pour l'équation de Perona-Malik,
    C. R. Acad. Sci. Paris, sér I, 344 (4) (2007) 225-229. Link to PDF
46. The Perona-Malik Method as an Edge Pruning Algorithm,
    Journal of Mathematical Imaging and Vision, 30 (2) (2008) 209-219. Link to PDF. Link to text.
47. Soliton Stars in the Breather Limit,
    Classical and Quantum Gravity, 25 (2008) 245004. Link to PDF. Other link.
48. Hypergeometric Functions and Singular Solutions of Wave Equations with Lorentz-invariant Potential,
    Communications in Contemporary Mathematics 11 (3) (2009) 447-458
    (with A. Bentrad). Link to PDF
49. Brahmagupta's Derivation of the Area of a Cyclic Quadrilateral,
    Historia Mathematica, 37 (1) (2010) 28-61. DOI, Link to PDF
50. Improving Hölder's Inequality,
    Houston Journal of Mathematics, 36 (1) (2010) 303-312. Link to PDF Other link to PDF
51. Review of Mathematics in India by Kim Plofker (Princeton University Press, 2009),
    Indo-Iranian Journal, 53 (4) (2010) 373-381. Link to PDF
52. Quelques aspects de l'œuvre de Bhārati,
    Journal Asiatique, 300 (1) (2012) 167-194
    (with S. Kichenassamy). Link
53. Brahmagupta's propositions on the perpendiculars of cyclic quadrilaterals,
    Historia Mathematica, 39 (4) (2012) 387-404. Link to PDF
54. L'Analyse Littéraire au service de l'Histoire des Mathématiques : Critique interne de la Géométrie de Brahmagupta,
    Comptes-Rendus des Séances de l'Académie des Inscriptions et Belles-Lettres, CRAI 2012, II (avril-juin) 781-796. (Communication du 20 avril 2012) Link to PDF
55. Textual Analysis of Ancient Indian Mathematics,
    Gaṇita Bhāratī, 33 (1) (2011) 15-28.
56. Brahmagupta's triquadrilateral,
    in : Proc. ISHM-2012 (International Seminar on the History of Mathematics, Ramjas College, University of Delhi, India, Nov. 19-20, 2012), pp. 33-35.
57. Control of Blow-up Singularities for Nonlinear Wave Equations,
    Evolution Equations and Control Theory, 2 (4) (2013) 699-677. Link to PDF
58. Le ''triquadrilatère'' de Brahmagupta : Analyse d'un texte mathématique,
    in Comptes Rendus du Séminaire d'Histoire des Mathématiques, 1 (2015) 47-66. Institut de Recherche sur l'Enseignement des Mathématiques (IREM) de Reims, janvier 2015 (ISBN: 978-2-910076-13-9). Link to PDF
59. Continued proportions and Tartaglia's solution of cubic equations,
    Historia Mathematica, 42 (4) (2015), 407-435. Link to PDF, Présentation dans les Actualités Scientifiques du CNRS.
60. Introduction à l'œuvre de S. Kichenassamy en Physique Théorique,
    Annales de la Fondation Louis de Broglie, 41 (2016), 131-151. Link to PDF
61. Une dialectique de l'être et du néant dans la philosophie tamoule médiévale : Hommage à S. Kichenassamy (1926-2015),
    Journal Asiatique, 306 (1) (2018), 85-99. Link to PDF
62. Le pāvai nōṉpu selon le Tiruppāvai, ou comment les rêves peuvent rencontrer la réalité, Journal Asiatique, 306 (2) (2018), 249-271.
    Link to PDF
63. Review of The Mathematics of India by P. P. Divakaran (Hindustan Book Agency, 2018),
    Gaṇita Bhāratī, 40 (2) (2018), 181-190.
64. Review of Les mathématiques de l'autel védique by Jean-Michel Delire (Droz, 2016),
    Aestimatio, 13 (2016-2018), 119-140. Link to PDF
65. Translating Sanskrit Mathematics,
    Aestimatio, N. S. 1 (2020), 183-204. DOI. Link to PDF
66. Mécanique ondulatoire et C-équivalence,
    Annales de la Fondation Louis de Broglie, 45 (1) (2020), 99-111. Link to PDF
67. L'irruption de l'infini : la légende de la colonne de lumière,
    Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres, CRAI 2018, IV (novembre-décembre), 1783-1799. (Communication du 7 décembre 2018). Link to PDF
68. Brahmagupta's apodictic discourse,
    Gaṇita Bhāratī, 41 (1) (2019), 93-113. DOI. Link to text.
69. Review of Karaṇapaddhati of Putumana Somayājī by Venketeswara Pai, K. Ramasubramanian, M.S, Sriram and M.D. Srinivas (Springer Nature and Hindustan Book Agency, 2018),
    Indian Journal of History of Science, 56 (2021) 149-153, published online 20 August, 2021. DOI. Link to text.
70. Hot Spots in the Weak Detonation Problem and Special Relativity,
    Axioms, 10 (4) (2021), 311. DOI. Link to PDF
    Reprinted in 10th anniversary of Axioms : Mathematical Physics, Hans J. Haubold (ed.), Basel: MDPI, 2023, pp. 79-95 (ISBN 978-3-0365-6867-6).
71. Apodictic discourse and the Cauchy-Bunyakovsky-Schwarz inequality,
    Gaṇita Bhāratī, 42 (1) (2020), 129-147. DOI.
72. О решении уравнения Лиувилля (1850, 1853) и его влиянии (On the solution of Liouville's equation (1850, 1853) and its impact)
    in Институт истории естествознания и техники им. С.И. Вавилова. Годичная научная конференция, 2021. М.: ИИЕТ РАН, 2021,
    R.A. Fando [Р.А. Фандо], E.V. Minina [Е.В. Минина ] and V.M. Savenkova [В.М. Савенкова], eds. (ISBN 978-5-6046393-4-4), pp. 81-86. (with E.M. Bogatov [Е.М. Богатов]). Link to English translation on HAL.
73. La vie de Ratnamati 勒那漫提 dans le Xu Gaoseng Zhuan 續高僧傳 et la transmission de savoirs mathématiques en contexte bouddhique,
    Journal des savants (2002), 2, 299-328 (with MA Ruixin 马瑞欣). HAL (CNRS archive).
74. Further Examples of Apodictic Discourse, I,
    Gaṇita Bhāratī, to appear.
75. Axiomatics of the Observer Manifold and Relativity,
    Axioms, 2023, 12 (2), 205 (16 pp.), Link to paper
76. Further Examples of Apodictic Discourse, II,
    Gaṇita Bhāratī, to appear.

1. L'histoire des mathématiques indiennes : impact sur l'enseignement,
   March 8, 2023, (IREM de Reims, Reims, France).
2. Further examples of Apodictic discourse,
   International Conference on History of Mathematics, November 25-27, 2022. (Indian Society for History of Mathematics, IIT Madras, Chennai, India.)
3. A critique of the notion of absolute beginning in Indian philosophy and iconography,
   Images and Stories of the Origin(s) of the World and Humankind. Organised by Prof. Dr Marion Gymnich and Prof. Dr Julia A. B. Hegewald (Bonn University, Germany). Online conference, 3-4 November, 2020. Conference page
4. Tunstall, Pacioli and Tartaglia's English Connection : Facts and Perspectives,
   Reappraising the ‘Art of Counting’. An international symposium to celebrate 500 years of Cuthbert Tunstall’s De arte supputandi libri quattuor. Organised by the British Society for the History of Mathematics and the Department of Mathematical Sciences at Durham University, Durham, U.K. (9-10 September 2022). Conference page
5. Liouville's hyperbolic and elliptic equations and their mathematical and physical interpretations (with E. M. Bogatov),
   Seminar on the History of Mathematics, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences (May 5, 2022). Link to video and slides in English and Russian.
6. What anyone should know about Indian Mathematics,
   Colloquium, April 15, 2022. This is part of the 75th anniversary celebrations of Indian independence.
7. The Euler-Poisson Darboux equations in the development of the theory of partial differential equations,
   Seminar on the History of Mathematics, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences (April 7, 2022). Link to video and slides in English and Russian.
8. Apodictic discourse and freedom of thought in Indian Mathematics,
   International Conference on History of Mathematics, December 16-18, 2021. (Indian Society for History of Mathematics, Department of Mathematics, Ramjas College, Delhi, India.)
9. Apodictic discourse : a new paradigm for rational communication?
   History of Mathematics Seminar Series IIT Gandhinagar, September 17, 2021.
10. Geometry without figures : Mathematics as apodictic discourse in Indian texts,
    International Conference on Ancient Indian Astronomy and Mathematics, with Special reference to Kerala, Sreekrishnapuram V.T. Bhattathiripad College, Mannampatta, Palakkad, India, July 26-28, 2021. Link to YouTube video

L'histoire des mathématiques indiennes : impact sur l'enseignement,

11. The Cauchy-Bunyakovsky-Schwarz inequality and its mathematical interpretations,
    Seminar on the History of Mathematics, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences (April 15, 2021). Link to video and slides in English and Russian See also article number 71.
12. On the impact of History on modern research and teaching.
    International web-conference on History of Mathematics, Delhi, India, December 20-22, 2020. Organized by the Indian Society for History of Mathematics. Slides on HAL.
13. Apodictic discourse in ancient and modern Mathematics.
    Online International Workshop on Srinivasa Ramanujan: The Man Beyond Infinity : Celebrating the National Mathematics Day on the occasion of 133th Birth Year of Srinivasa Ramanujan. (Central University of Himachal Pradesh, Shahpur, India), December 22, 2020.
14. Brahmagupta's Apodictic Discourse,
    ICHDMAST 2019 (International Conference on the History and Recent Developments in Mathematics with Applications in Science and Technology), New Vallabh Vidyanagar (India), December 17-19, 2019.
15. Lectures at the Chennai Mathematical institute (Chennai, India, December 4, 6 and 8, 2019).
    • Recent progress on the analysis of ancient Indian mathematical texts.
    • The impact and modern relevance of ancient Indian mathematics.
    • Algebraic aspects of Fuchsian Reduction.
16. Henry Thomas Colebrooke and the nature of Brahmagupta's mathematical discourse,
    H.T. Colebrooke and Historiographies of Sciences in Sanskrit, Apr. 15-16, 2019, Univ. Paris Diderot. Link Other link
17. Les problèmes indéterminés en Inde,
    Séminaire Histoire et Philosophie des Sciences, U. Paris Diderot (March 11, 2019).
18. L'Analyse comme discipline, héritière de l'algèbre et de la géométrie,
    Séminaire d'Histoire des Mathématiques, Université de Marne-la-Vallée (April 25, 2017).
19. L'articulation des concepts, des objets et des pratiques mathématiques : quelques exemples,
    Séminaire Histoire et Philosophie des Sciences, U. Paris Diderot (February 20, 2017).