This paper deals with a semilinear weighted parabolic problem in general bounded domains, subject to zero Dirichlet boundary conditions, where the weighted functions depend not only on space variable but also on time variable. Fujita exponents for blow-up and global existence of solutions are determined by using semigroup methods and the comparison principle, which are composed by the dimensions of the space domains and the eight exponents in nonlinear coupled sources and the space–time weighted functions.

中文翻译：

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有限域中时空加权抛物线问题的Fujita指数

本文在零狄里克雷边界条件下处理一般有界域中的半线性加权抛物线问题，其中加权函数不仅依赖于空间变量而且依赖于时间变量。采用半群方法和比较原理确定了Fujita指数的爆炸性和整体解的存在性，它们由空间域的维数和非线性耦合源中的八个指数以及时空加权函数组成。