一类非线性抛物方程的整体解和爆破解  

Global and Blow up Solutions for a Class of Nonlinear Parabolic Equations

作　　者：吴洁 崔泽建[1] WU Jie;CUI Zejian(College of Mathematic and Information,China West Normal University,Nanchong,Sichuan, China 637000)

机构地区：[1]西华师范大学数学与信息学院

出　　处：《昆明学院学报》2019年第3期74-81,共8页Journal of Kunming University

基　　金：四川省教育厅自然科学基金资助项目(09ZA119)

摘　　要：在罗宾边界条件和狄利克雷边界条件下,探讨了一类非线性抛物型方程的整体解和爆破解.采用的方法主要是根据给出的适当假设,通过构造恰当的辅助函数,并利用最大值原理及微分不等式技巧等,从而得到了该方程整体存在的充分条件及爆破解,同时,还给出了整体存在性解决方案的上估计和当爆炸发生时爆炸时间的上界.The global and blow up solutions for a class of nonlinear parabolic equations with Robin boundary condition and Dirichlet boundary condition are studied. The study method is mainly based on the appropriate assumptions given, by constructing exact auxiliary functions, using the maximum principle and differential inequality techniques to obtain the sufficient condition for global solution of this equation and blow up solution. Meanwhile, the upper estimate of the global solution and the upper bound for “blow up time” are also provided.

关 键 词：非线性抛物方程 极大值原理 爆破解 整体存在性 

分 类 号：O175.26[理学—数学]