一类半线性热方程整体解的存在性

Existence of Global Solution for a Class of Semi-linear Thermal Equation

研究了一类推广的半线性热方程的初边值问题。由于能量是非正定的,传统的Galerkin方法无法得到先验估计。将Galerkin方法与位势井理论结合,最终证明问题整体弱解的存在性,补充和推广了现有结论,并为研究此类方程提供一个方法上的借鉴。

In this paper, the initial boundary value problem of a generalized semi-linear thermal equation is studied. However, the energy is non-positive, it is hard to obtain the priori estimate by using the traditional Galerkin method. In this paper the existence of the global weak solution is proved by combining the potential well theory with Galerkin method, which supplements or extends the existing conclusions, and provides a method reference for studying such equations.