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March/April 2014 Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations
Yachun Li, Qin Wang, Zhigang Wang
Adv. Differential Equations 19(3/4): 387-408 (March/April 2014).

Abstract

We study the well-posedness of renormalized entropy solutions for quasilinear anisotropic degenerate parabolic-hyperbolic equation of the type $\partial_{t}u+\text{div}f(u)=\nabla\cdot(a(u)\nabla u)$ in a bounded domain with general $L^{1}$ initial data and homogeneous Dirichlet boundary condition. We use the device of doubling variables to prove the uniqueness and use the vanishing viscosity method to prove the existence.

Citation

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Yachun Li. Qin Wang. Zhigang Wang. "Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations." Adv. Differential Equations 19 (3/4) 387 - 408, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

MathSciNet: MR3161666

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Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 3/4 • March/April 2014
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