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| ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS |
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Citation： |
T. GALLOU\"ET,F. HUBERT.ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS[J].Chinese Annals of Mathematics B,1999,20(1):7~10 |
| Page view： 989
Net amount： 660 |
Authors： |
T. GALLOU\"ET; F. HUBERT |
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| Abstract： |
The authors give a proof of the convergence of the solution of the parabolic approximation $u^\eps_t+\div f(x,t,u^\eps)=\eps \lap u^\eps$ towards the entropic solution of the scalar conservation law $u_t+\div f(x,t,u)=0$
in several space dimensions. For any initial condition $u_0\in L^\infty(\R^N)$ and for a large class of flux $f$, they also prove the strong converge in any $L^p_{\text{loc}}$ space, using the notion of entropy process solution,which is a generalization of the measure-valued solutions of DiPerna. |
Keywords： |
Convergence, Parabolic approximation, Conservation law |
Classification： |
35A35, 35K30 |
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