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2010年02月26日

【期刊论文】Evolutionary weighted p-Laplacian with boundarydegeneracy ✩

王春朋， Yin Jingxue， Wang Chunpeng ∗

J. Differential Equations 237(2007)421-445，-0001，（）：

-1年11月30日

The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems.

Evolutionary weighted p-Laplacian， Boundary degeneracy， Hyperbolic， Parabolic

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2010年02月26日

【期刊论文】Uniqueness of the bounded solution to a strongly degenerateparabolic problemI

王春朋， Qiang Liua， Chunpeng Wangb， _

Nonlinear Analysis 67(2007)2993-3002，-0001，（）：

-1年11月30日

摘要

This paper concerns the uniqueness of the bounded solution to a strongly degenerate parabolic problem. The equation consideredmay have two kinds of strong degeneracies and there is no restriction on the relation between the two degeneracies. By usingHolmgren’s approach, we prove that the bounded solution of the associated initial–boundary value problem is unique under someessentially necessary condition on the growth of the convection.

Uniqueness， Bounded solution， Strong degeneracy

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2010年02月26日

【期刊论文】Critical exponents of the non-Newtonian polytropic filtrationequation with nonlinear boundary condition✩

王春朋， Wang Zejiaa， b， Yin Jingxuea， Wang Chunpenga， ∗

Applied Mathematics Letters 20(2007)142-147，-0001，（）：

-1年11月30日

摘要

This work is concerned with the critical exponent of the non-Newtonian polytropic filtration equation with nonlinear boundary conditions. We obtain the critical global existence exponent and critical Fujita exponent by constructing various self-similar supersolutions and subsolutions.

Non-Newtonian polytropic filtration equation， Nonlinear boundary flux， Global existence， Blow-up， Critical exponent

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2010年02月26日

【期刊论文】Critical Fujita exponents of degenerate andsingular parabolic equations

王春朋， Chunpeng Wang， Sining Zheng

Proceedings of the Royal Society of Edinburgh, 136A, 415-430, 2006，-0001，（）：

-1年11月30日

摘要

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2010年02月26日

【期刊论文】Renormalized Solutions of a Nonlinear ParabolicEquation with Double Degeneracy_

王春朋， Zejia Wang，， Yinghua Li† and Chunpeng Wang

Electronic Journal of Qualitative Theory of Differential Equations 2006, No.5, 1-12，-0001，（）：

-1年11月30日

摘要

In this paper, we consider the initial-boundary value problem of a nonlinear parabolic equation with double degeneracy, and establish the existence and uniqueness theorems of renormalized solutions which are stronger than BV solutions.

Renormalized solutions,， double degeneracy.，

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