Lectures: Monday- 15:30-16:55, Thursday- 15:30-16:55, Class room- 113
Office Hours: Monday- 17:30-18:30
Contact: Office room 115 A, Mathematics Dept., IIT Bombay, Powai, Email: deban@math.iitb.ac.in.
Objectives:
1. Hyperbolic conservation laws: Basic Concepts: Definition and examples, Loss of regularity, Weak solution, Rankine-Hugoniot jump condition, Entropy solution.
2. Scalar Conservation Laws: Existence of an entropy solution, Uniqueness of the entropy solution, Asymptotic behavior of the entropy solution, The Riemann problem.
3. System of Conservation Laws: Linear hyperbolic system with constant coefficients, Nonlinear case, Simple waves and Riemann invariants, Shock waves and contact discontinuities, Characteristic curves and entropy conditions, Solution of the Riemann problem, The Riemann problem for the p-system.