EXISTENCE OF STRONG TRACES FOR GENERALIZED SOLUTIONS OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS

In the half-space t > 0 a multidimensional scalar conservation law with only continuous flux vector is considered. For the wide class of functions including generalized entropy sub- and super-solutions to this equation, we prove existence of the strong trace on the initial hyperspace t = 0. No nondegeneracy conditions on the flux are required.

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AN EQUAL-AREA METHOD FOR SCALAR CONSERVATION LAWS

The ANZIAM Journal ◽

10.1017/s1446181112000065 ◽

2011 ◽

Vol 53 (2) ◽

pp. 156-170

Author(s):

MARJETA KRAMAR FIJAVŽ ◽

MITJA LAKNER ◽

MARJETA ŠKAPIN RUGELJ

Keyword(s):

Conservation Law ◽

Simple Algorithm ◽

Characteristic Surface ◽

Scalar Conservation Laws ◽

Equal Area ◽

One Dimensional ◽

Scalar Conservation ◽

The One ◽

Integral Version ◽

Class Of Functions

AbstractWe study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. A simple algorithm for computing the unique solution is developed. The method uses the equal-area principle and yields the solution for any given time directly.

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EXISTENCE OF STRONG TRACES FOR QUASI-SOLUTIONS OF MULTIDIMENSIONAL CONSERVATION LAWS

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891607001343 ◽

2007 ◽

Vol 04 (04) ◽

pp. 729-770 ◽

Cited By ~ 57

Author(s):

E. YU. PANOV

Keyword(s):

Conservation Laws ◽

Wide Class ◽

Conservation Law ◽

Generalized Entropy ◽

Class Of Functions

We consider a conservation law in the domain Ω ⊂ ℝn+1 with C1 boundary ∂Ω. For a wide class of functions including generalized entropy sub- and super-solutions, we prove the existence of strong traces for normal components of the entropy fluxes on ∂Ω. Non-degeneracy conditions on the flux are not required.

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Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

Abstract and Applied Analysis ◽

10.1155/2009/350762 ◽

2009 ◽

Vol 2009 ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

V. G. Danilov ◽

D. Mitrovic

Keyword(s):

Approximate Solution ◽

Initial Data ◽

Conservation Laws ◽

Asymptotic Method ◽

Nonlinear Waves ◽

Conservation Law ◽

Scalar Conservation Laws ◽

Scalar Conservation Law ◽

Scalar Conservation ◽

Smooth Approximations

We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.

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