多维非齐次广义BBM方程的初边值问题

Initial Boundary Value Problem for One Class of Multidimensional Inhomogeneous Generalized BBM Equations

本文考虑如下多维非齐次广义BBM 方程的初边值问题{u_f-△U_t=F(u,▽u) t>o x∈Ω,(1.1)u(0,x)=g(x) x∈Ω,(1.2)(?)/(?)|(?)=(?)(x) t≥0,(1.3)这里Ω是R^n 中有界域,v 是(?)上的外法线方向,▽u=(u_x_1,…u_(x_(?)),通过引入爆破因子k(u),我们讨论了问题(1.1)、(1.2),(1.3)在有限时间内解的爆破情况.

This paper considers the following initial-boundary value problem for one classof multidimensional inhomogeneous generalized BBM equations(?)u_t-△u_t=F(u,▽u)t>0 x∈Ω, (1.1)u(0,x)=g(x) x∈Ω,(1.2)(?)u/(?)v(?)Ω=0 t≥0,(1.3)Where Ω is a bounded domain in R^u,v is the out-ward normal on (?)Ω,▽u=(u_x_1,…,u_x_n).By introducing the blowing-up fact,the blowing-up behaviours of thesolutions in finite time for the problem(1.1),(1.2),(1.3)are investigated.