A kinetic approach to error estimate for nonautonomous anisotropic degenerate parabolic-hyperbolic equations

Xingwen Hao; Yachun Li; Qin Wang

doi:10.3934/krm.2014.7.477

Article Contents

2014, Volume 7, Issue 3: 477-492. Doi: 10.3934/krm.2014.7.477

This issue Previous Article Numerical simulations of degenerate transport problems Next Article Hysteretic behavior of a moment-closure approximation for FENE model

A kinetic approach to error estimate for nonautonomous anisotropic degenerate parabolic-hyperbolic equations

1.
School of Mathematics and Information Sciences, Weifang University, Weifang 260240
2.
Department of Mathematics and Key Lab of Scientific and Engineering Computing (MOE), Shanghai Jiao Tong University, Shanghai 200240
3.
Department of Mathematics, Yunnan University, Kunming 650091

Received: November 2013

Revised: June 2014

Published: September 2014

Abstract / Introduction Related Papers Cited by

Abstract

This paper is devoted to the error estimate of approximate solutions for non-autonomous degenerate parabolic-hyperbolic equations, where the nonlinear convection flux, the diffusion matrix and source term depend on time $t$ explicitly. Our method is based on kinetic formulation and kinetic entropy formula. By developing the kinetic techniques, we obtain an error estimate of order $O(\sqrt{\mu})$, where $\mu$ is the artificial viscosity.

Keywords:

Degenerate parabolic-hyperbolic equation,
kinetic formulation,
entropy solution,
error estimate.

Mathematics Subject Classification: Primary: 35B30, 35B51, 35K65; Secondary: 35B35.

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