一类拟线性抛物型偏微分方程的解

The Solution for a Class of Quasi-Linear Parabolic Partial Differential Equations

建立了一类拟线性抛物性方程初边值问题的比较原理,从而利用单调方法证明了具有齐次Dirichlet边值条件的拟线性抛物型偏微分方程解的存在唯一性;同时也运用第一特征函数构造上、下解的方法讨论具体的拟线性抛物型方程解的爆破现象.参9.

The author established comparison principle on quasi - linear parabolic partial differential equations with initial boundary value problems, thereby proved the existence and uniqueness of solutions for quasi - linear parabolic partial differential equations in bounded domain with homogeneous Diriehlet boundary conditions by utilizing monotone methods. Meanwhile, we made use of upper and lower solution which be obtained by the first eigenfunetion to discuss the solution blow -uo ohenomenon. 9refs.