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Hamilton-Jacobi equations and viscosity solutions Description

Key Elements

Code

MEDP 511

Formation

M2 Partial Differential Equations and Numerical Analysis

Semester

1

Credits

4

Number of Teaching Hours

28

Number of Tutoring Sessions

0

Number of Laboratory Sessions

0

Content

Objective

Content

1. Preliminaries: the method of characteristics 2. Definitions and properties of viscosity solutions 2.1. Case of elliptic second order equation 2.2. Case of parabolic second order equation 2.3. Definition based on sub- and super-differentials 2.4. Stability properties 2.5. The half-relaxed limits 2.6. The vanishing viscosity technique 3. Uniqueness results 3.1. Comparison principle 3.2. First uniqueness result: a simple setting 3.3. Uniqueness result: general first order equations 4. Existence by Perrons method 4.1. Sup and Inf operations 4.2. Perrons method: special assumptions 4.3. General Perrons method 4.4. Existence of continuous viscosity solution 5. Application of viscosity solutions to front propagation