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Large time behaviour of solutions of scalar viscous and nonviscous conservation laws

✍ Scribed by M. Bertsch; J. Goncerzewicz; D. Hilhorst

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
246 KB
Volume
12
Category
Article
ISSN
0893-9659

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✦ Synopsis

We study the large time behaviour of entropy solutions of the Cauchy problem for a possibly degenerate nonlinear diffusion equation with a nonlinear convection term. The initial function is assumed to have bounded total variation. We prove the convergence of the solution to the entropy solution of a Riemann problem for the corresponding first-order conservation law. (~) 1999 Elsevier Science Ltd. All rights reserved.

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Solutions of Hamilton–Jacobi Equations a
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✍ Daniel N. Ostrov πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 235 KB

We establish a unique stable solution to the Hamilton-Jacobi equation x 2 ðÀ1; 1Þ; t 2 Β½0; 1Þ with Lipschitz initial condition, where KΓ°x; tÞ is allowed to be discontinuous in the Γ°x; tÞ plane along a finite number of (possibly intersecting) curves parameterized by t: We assume that for fixed k;