关于Fujita类方程组解的有界性和Blow up的一些结论

Some Result of Boundedness and Blow up for A Semilinear Reaction Diffusion Systems of Fujita Type

对Fujita类方程组解的整体存在性和如何在有限时间内发生Blow up现象的研究,具有实际意义.M.Escobedo等人对其二元情形曾做过研究,即在[1]中对非线性项单一如v^(?)或u^(?)的Cauchy问题进行了讨论,本文意在上述基础上作些推广:修改非线性项如u^(?)v^(?)或u^qv^n情形,利用上、下解的方法,证明了在一定条件下,推广后的Cauchy问题亦有[1]中指出的类似的结果.

It is very useful for application to discuss the global solution exsitence and finite time blow up of Fujita type systems. M. Escobedo and M. A. Herrero have considered binary systems in [1] but only considered that nonlinear terms are v^p and u^q . We show in this paper what happen when the nonlinear terms are u^q v^p and v^p u^q . Using a construction method for obtaining sub and super solutions, we prove-that under restriction to p,q,m,n.u_o(x) ,v_o(x ), we have some similar results in [1].