一类半线性抛物方程的解的爆破性质研究

Research on the Blasting Solution of a Class of Semilinear Parabolic Equations

摘要: 本文通过变量指数函数来研究一类半线性抛物方程的局部解的爆破性质。在齐次狄利克雷条件的有限域中，变量指数函数认为是非负有界的。通过指数函数的边界条件，可以确定半线性抛物方程局部解在大初始数据条件和任意初始数据条件下爆破的条件。最后，对方程所有爆破性质进行总结，证明所分析的方程满足一个Fujita类型的结论，即方程的解可以在变量指数函数和域的大小这些条件确定的任意非平凡初始数据中产生爆破。

Abstract: This article uses the variable index function to research the local solution of a class of semilinear parabolic equations of the blasting quality. In the limited domain of homogeneous Dirichlet condi-tion, variable index function is the non-negative and bounded. With boundary condition of expo-nential function, we can define the local solution of semilinear parabolic equation at the condition of big initial data and arbitrary initial data of blasting conditions. Finally, we summarize all blasting properties about equations, and it was proved that the equation satisfies a Fujita type of conclusion; namely equation solution can be blasting in the variable index function and the size of domain that conditions of the nontrivial initial data are determinated.