一类半线性抛物边值问题的最大值原理

Acta mathematica scientia,Series A ›› 2004, Vol. 24 ›› Issue (1): 63-70.

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Maximum |Principles for a Class of Semilinear Parabolic Boundary Value Problems

DING Jun-Tang

Online:2004-02-25 Published:2004-02-25
Supported by:
国家自然科学基金(60174007)；山西省自然科学基金和山西大学青年科技基金资助项目.

Abstract

Abstract:

By constructing an auxiliary function defined on solutions of the semilinear par abolic equations u_t=Δu+f(x,u,q,t) (q=|u|^2),subject to nonnegative initial date and either Dirichlet or Neumann boundary conditions, and using Hopf's maximum pr inciples and Riemannian geometry theorm on it, the maximum principles of this fu nction are obtained. The estimation of gradient q and the estimation of the solution u are given.

Key words: Semilinear parabolic equation, Solution, Gradient of the solution; , Maximum principles

CLC Number:

35B50

DING Jun-Tang. Maximum |Principles for a Class of Semilinear Parabolic Boundary Value Problems[J].Acta mathematica scientia,Series A, 2004, 24(1): 63-70.

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Maximum |Principles for a Class of Semilinear Parabolic Boundary Value Problems

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