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Partial Differential Equations, MA606
Instructor
Dr. Pawan Kumar Mishra,
email:pawan@iitbhilai.ac.in
Phone: +919118498909
Room No: 311B
Timing and Venue
Day: Thursday and Friday, Time: 2:30 pm-3:50 pm
The course will run in ONLINE mode. The Webex link to join the class is https://iitbhilai.webex.com/meet/b107
Course Content
Module -1
First-order PDE:
Method of characteristics and existence of local solutions. Hamilton Jacobi equation, Hopf-Lax formula, weak solution of Hamilton-Jacobi equation and its uniqueness;
Introduction to conservation laws, weak solutions, Rankine-Hugoniot condition, shocks, Lax-Oleinik formula, entropy condition and uniqueness of entropy solution.
Characteristic Manifolds and Cauchy Problem, non-characteristic surfaces, Cauchy-Kowalevski theorem and uniqueness theorem of Holmgren.
Module -2
Second order PDE:
Laplace and Poisson's Equation:
fundamental solution, harmonic function and its properties; Dirichlet problem and Greens function; existence of solution of the Dirichlet problem using Perron's method; Introduction to variational method;
Module -3
Heat Equation: fundamental solution and initial-value problem; mean value formula, maximum principle, uniqueness and regularity; nonnegative solutions;
Wave Equation in dimension one: d'Alemberts formula, method of spherical means, Hadamard's method of descent, Duhamel's principle and Cauchy problem, initial-boundary-value problem.
References
Lawrence C. Evans, Partial Differential Equations: Second Edition
Robert McOwen, Partial Differential Equations: Methods and Applications, 2nd Edition
Phoolan Prasad and Renuka Ravindran, Partial Differential Equations
A. K. Nandakumaran and P. S. Datti, Partial Differential Equations: Classical Theory with Modern Touch
Evaluation
There will be two tierce exams (1st tierce and 3rd tierce) of 25% and 30% weightage. Apart from tierce exams there will be 3 quizzes each of 10% weightage and 1 assignment of 15% weightage of total marks.
Lecture Notes and Tutorials
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