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December  2009, 25(4): 1275-1286. doi: 10.3934/dcds.2009.25.1275

Strong traces for degenerate parabolic-hyperbolic equations

Young-Sam Kwon 1,

1. 

Department of Mathematics, Dong-A University, Busan 604-714, South Korea

Received  April 2008 Revised  July 2009 Published  September 2009

In this paper we consider bounded weak solutions $u$ of degenerate parabolic-hyperbolic equations defined in a subset $]0,T[\times\Omega\subset \R^{+}\times \R^d$. We define a strong notion of trace at the boundary $]0,T[\times\partial\Omega$ reached by $L^1$ convergence for a large class of functionals of $u$ and at $0 \times \Omega$ reached by $L^1$ convergence for solution $u$. This result develops the strong trace results of Kwon, Vasseur [13] and Panov [19, 20] for more general equations, namely, degenerate parabolic-hyperbolic equations.
Keywords: kinetic formulation, trace theorem, boundary value problem., $H$-measure, Degenerate parabolic-hyperbolic equation, conservation law.
Mathematics Subject Classification: 35K20, 35K55, 35L65, 35K6.
Citation: Young-Sam Kwon. Strong traces for degenerate parabolic-hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1275-1286. doi: 10.3934/dcds.2009.25.1275
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