数学
常微分方程
数学分析
偏微分方程
反应扩散系统
非线性系统
上下界
扩散
应用数学
微分方程
物理
热力学
量子力学
作者
R. Saranya,N. Annapoorani
出处
期刊:Springer proceedings in mathematics & statistics
日期:2023-01-01
卷期号:: 67-78
标识
DOI:10.1007/978-981-19-7272-0_6
摘要
AbstractThis paper is concerned with the blow-up phenomena and global existence of a fractional nonlinear reaction-diffusion equation with a non-local source term. Under sufficient conditions on the weight function a(x) and when the initial data is small enough, the global existence of solutions is proved using the comparison principle. We establish a finite time blow-up of the solution with large initial data by converting the fractional PDE into a simple ordinary differential inequality using the differential inequality technique. Moreover, by solving the obtained ordinary differential inequality, an upper bound of the blow-up time is also deduced.KeywordsBlow-upGlobal existenceFractional partial differential equation
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