Semestre 2022-1
Nonlinear Hyperbolic Partial Differential Equations
Advanced Graduate Course on Differential Equations
Posgrado en Ciencias Matemáticas (UNAM)
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Online classes
Introduction and General Information
Section I: Nonlinear first order PDE
Method of characteristics Loss of regularity Fully nonlinear Hamilton-Jacobi equations I H-J equations II H-J equations III
Section II: Scalar conservation laws
Entropy condition Lax-Oleinik formula Lax-Oleinik formula as entropy solution Uniqueness of entropy solutions
Riemann's problem Long time behavior
Section III: System of conservation laws
Introduction to system of conservation laws Integral solutions and hyperbolic systems Hyperbolic systems II
Simple and rarefaction waves The shock set Contact discontinuities, shock waves and Riemann's problem Entropy criteria
Section IV: Nonlinear wave equations
Conservation of energy and finite propagation speed Sobolev spaces and weak solutions Existence of solutions