Convergence of approximate solutions to conservation laws. (English) Zbl 0519.35054

DiPerna, R. J.

Arch. Ration. Mech. Anal. 82, 27-70 (1983).

MSC:

35L65	Hyperbolic conservation laws
35A35	Theoretical approximation in context of PDEs
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99	Numerical methods for partial differential equations, boundary value problems
35B35	Stability in context of PDEs
35B45	A priori estimates in context of PDEs
35L60	First-order nonlinear hyperbolic equations
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
60B05	Probability measures on topological spaces
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
74B20	Nonlinear elasticity
76L05	Shock waves and blast waves in fluid mechanics
76N15	Gas dynamics (general theory)

Keywords:

convergence; approximate solutions; systems of conservation laws; compensated compactness; parabolic regularization; finite difference schemes in conservation form

Citations:

Zbl 0399.46022; Zbl 0437.35004

References:

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