广义神经传播型非线性拟双曲方程解的爆破

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Blow-up of Solutions of Nonlinear Pseudo-Hyperbolic Equations of Generalized Nerve Conduction Type

摘要: 本文讨论了广义神经传播型非线性拟双曲方程u_tt-Δu_t=F(x,t,u,∇u,u_t,∇u_t)分别具Neumann边界和Dirichlet边界的两类混合问题.在非线性部分F(x,t,u,∇u,u₁,∇u₁)和初值满足某些条件时,我们得到了解的爆破性质.

Abstract: This paper deals with the two types of mixed problems with respect to Neumann boundary and Dirichlet boundary for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type u_tt-Δu_t=F(x,t,u,∇u,u_t,∇u_t) when the nonlinear part F(x,t,u,∇u,u_t,∇u_t) and the initial values satisfy some conditions, the blow-up properties of the solytions are obtained.

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