一类半线性抛物方程的解的爆破性质研究.pdfVIP

Advances in Applied Mathematics 应用数学进展, 2017, 6(1), 10-19 Published Online January 2017 in Hans. /journal/aam /10.12677/aam.2017.61002 Research on the Blasting Solution of a Class of Semilinear Parabolic Equations 1 2 Liang Zhang , Jianjun Li 1 College of Science, Inner Mongolia University of Technology, Hohhot Inner Mongolia 2 College of Science, Liaoning Technical University, Fuxin Liaoning th th th Received: Dec. 20 , 2016; accepted: Jan. 9 , 2017; published: Jan. 16 , 2017 Copyright © 2017 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Open Access 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 blast- ing properties about equations, and it was proved that the equation satisfies a Fujita type of con- clusion; 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. Keywords Semilinear Parabolic Equations, Variable Index Function, The Conclusion of the Fujita 一类半线性抛物方程的解的爆破性质研究 1 2 张 亮 ，李建军 1 内蒙古工业大学理学院，内蒙古 呼和