方程u_t=u_(xxt)+σ(u_x)_x含第二类边界条件的初边值问题(Ⅰ)—整体强解的存在与唯一性

Initial-Boundary Value Problems of Equation u_t= u_(xxt)+ σ(u_x)_x Including Second Boundary Conditions (I)-Existence and Uniqueness of Global Strong Solution

本文研究Sobolev-Galpern型方程u_t=u_(xxt)+σ(u_x)_x具边界条件u_x(0,t)=u_x(1,t)=0与u(0,t)=u_x(1,t)=0的初边值问题,设σ∈C^1,σ~1(S)下方有界,得到整体强解的存在唯一性.

This paper studies the initial -boundary value problems of equation of Sobolev-Galpern type ut=uxxt +(ux)x with boundary conditions ux(0,ti) =ux(1,t) = 0 and u(0,t) = ux[(l,t) = 0. Suppose that σ∈C', σ '(s) is lower bounded, then we can obtain the existence and uniqueness of the global strong Solution.