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Diffraction problems for quasilinear parabolic systems with boundary intersecting interfaces

Qi-Jian Tan* and Chao-Yi Pan

Author Affiliations

Department of Mathematics, Chengdu Normal University, Chengdu, 611130, P.R. China

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Boundary Value Problems 2013, 2013:99  doi:10.1186/1687-2770-2013-99

Published: 22 April 2013

Abstract

In this paper, we discuss the n-dimensional diffraction problem for weakly coupled quasilinear parabolic system on a bounded domain Ω, where the interfaces <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/99/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/99/mathml/M1">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/99/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/99/mathml/M2">View MathML</a>) are allowed to intersect with the outer boundary Ω and the coefficients of the equations are allowed to be discontinuous on the interfaces. The aim is to show the existence of solutions by approximation method. The approximation problem is a diffraction problem with interfaces, which do not intersect with Ω.

MSC: 35R05, 35K57, 35K65.

Keywords:
diffraction problem; quasilinear parabolic system; interface; approximation method