具有非局部源与加权非局部边界条件的拟线性抛物方程组

A Quasilinear Parabolic System with Nonlocal Sources and Weighted Nonlocal Boundary Conditions

中文关键词:  拟线性抛物方程组  非局部边界条件  临界指标  blow-up速率  权函数.

英文关键词:quasilinear parabolic system  nonlocal boundary conditions  critical exponent  blow-up rate  weight functions.

中文摘要:

      本文研究具有非局部非线性源与加权非局部边界条件的反应扩散方程组的blow-up性质。在权函数的不同情形下建立临界指标。可以看出，边界权函数在确定blow-up条件时起重要作用。此外，还得到非局部解的blow-up速率，该速率与非线性扩散参数$m$和$n$无关。

英文摘要:

      In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In addition, the blow-up rate estimate of non-global solutions for a class of weight functions is also obtained, which is found to be independent of nonlinear diffusion parameters $m$ and $n$.