Partial Differential Equations

A. K. Nandakumaran is a Professor in the Department of Mathematics, Indian Institute of Science, Bengaluru. He obtained his Masters degree from Calicut University, Kerala and then worked for his Ph.D. in Tata Institute of Fundamental Research and Indian Institute of Science. His general area of research includes partial differential equations and special areas include homogenization, control and controllability problems, inverse problems and computations. His work also includes tomographic reconstruction problems. He is a Press author of the book Ordinary Differential Equations: Principles and Applications (2017). He is a Fellow of National Academy of Sciences India (NASI) and convener of Kishore Vaigyanik Prothsahan Yojana (KVPY). P. S. Datti is a Former Professor at TIFR Centre for Applicable Mathematics, Bengaluru. After obtaining M.Sc. in 1976 from Karnatak University, Dharawad, he joined the then TIFR-IISc Joint Programme in Applications of Mathematics as a research student. He then moved to the Courant Institute of Mathematical Sciences for his Ph.D. His main areas of research interest include nonlinear hyperbolic equations, hyperbolic conservation laws, ordinary differential equations, evolution equations and boundary layer phenomenon. He has written TIFR Lecture Notes for the lectures delivered by G.B. Whitham (CalTech) and Cathleen Morawetz (Courant Institute). He is a Press author of the book Ordinary Differential Equations: Principles and Applications (2017).

• List of illustrations; Preface; Acknowledgements; Notations; 1. Introduction; 2. Preliminaries; 3. First-order partial differential equations: method of characteristics; 4. Hamilton–Jacobi equation; 5. Conservation laws; 6. Classification of second-order equations; 7. Laplace and Poisson equations; 8. Heat equation; 9. One-dimensional wave equation; 10. Wave equation in higher dimensions; 11. Cauchy–Kovalevsky theorem and its generalization; 12. A peep into weak derivatives, Sobolev spaces and weak formulation; References; Index.