一般非线性渗流方程广义解的存在唯一性与Blow-up

数学季刊 ›› 2008, Vol. 23 ›› Issue (2): 301-308.

一般非线性渗流方程广义解的存在唯一性与Blow-up

Department of Mathematics,Zhongyuan Institute of Technology

收稿日期:2006-04-28 出版日期:2008-06-30 发布日期:2023-10-10
作者简介: HUO Zhen-hong(1963-), male, native of Pingyu, Henan, a lecturer of Zhongyuan Institute of Technology, M.S.D., engages in the theories of nonlinear partial differential equations.
基金资助:
Supported by National Science Foundation of China(10572156); Supported by Natural
Science Foundation of Henan Province(0211010900); Supported by National Science Foundation of Department
of Education of Henan Province(200510465001)

Existence, Uniqueness and Blow-up of Generalized Solutions to General Nonlinear Filtration Equations

Department of Mathematics,Zhongyuan Institute of Technology

Received:2006-04-28 Online:2008-06-30 Published:2023-10-10
About author:HUO Zhen-hong(1963-), male, native of Pingyu, Henan, a lecturer of Zhongyuan Institute of Technology, M.S.D., engages in the theories of nonlinear partial differential equations.
Supported by:
Supported by National Science Foundation of China(10572156); Supported by Natural
Science Foundation of Henan Province(0211010900); Supported by National Science Foundation of Department
of Education of Henan Province(200510465001)

摘要/Abstract

摘要： In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations u_t-D_j(a^ij(x,t,u)D_i+(u))+bⁱ(t,u)D_iu+C(x,t,u)=0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.

关键词: nonlinear filtration equation, Cauchy problem, generalized solution, existence;
uniqueness, blow-up

Abstract: In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations u_t-D_j(a^ij(x,t,u)D_i+(u))+bⁱ(t,u)D_iu+C(x,t,u)=0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.

Key words: nonlinear filtration equation, Cauchy problem, generalized solution, existence;
uniqueness, blow-up

中图分类号:

霍振宏, 李海峰. 一般非线性渗流方程广义解的存在唯一性与Blow-up[J]. 数学季刊, 2008, 23(2): 301-308.

HUO Zhen-hong, LI Hai-feng. Existence, Uniqueness and Blow-up of Generalized Solutions to General Nonlinear Filtration Equations [J]. Chinese Quarterly Journal of Mathematics, 2008, 23(2): 301-308.

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