Initial boundary value problem for generalized boussinesque type equations with nonlinear source

被引：0

作者：

A. I. Kozhanov

机构：

[1] Siberian Division of the Russian Academy of Sciences,Institute of Mathematics

来源：

Mathematical Notes | 1999年 / 65卷

关键词：

initial boundary value problem; Boussinesque equation; comparison principle;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A comparison principle for solutions of the first initial boundary value problem for the generalized Boussinesque equation with a nonlinear sourceut-Δψ(u)-Δut+q(u)=0 is established. By using this comparison principle, we prove new existence and nonexistence theorems for solutions of the first initial boundary value problem in the case of power-law functions ψ (ξ) andq (ξ).

引用

页码：59 / 63

页数：4

共 4 条

[1]

Dzekker E. S.(1972)A generalization of the equation describing the motion of underground water with a free boundary Dokl. Akad. Nauk SSSR [Soviet. Math. Dokl.] 202 1031-1033

[2]

Furaev V. Z.(1983)On global solvability of the first boundary value problem for the generalized Boussinesque equation Differentsial’nye Uravneiya [Differential Equations] 19 2014-2015

[3]

Gladkov A. L.(1988)The Cauchy problem in the class of increasing functions for several nonlinear pseudoparabolic equations Differentsial’nye Uravneniya [Differential Equations] 24 277-288

[4]

Kozhanov A. I.(1994)Parabolic equations with a nonlinear nonlocal source Sibirsk. Mat. Zh. [Siberian Math. J.] 35 1062-1073

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