Blow-up and global existence for semilinear parabolic equations on infinite graphs
Abstract
We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function f(u). We always assume that the infimum of the spectrum of the Laplace operator λ1(G) on the graph is positive. According to an interaction between the behavior of f close to 0 and the value λ1(G), we get the existence of a global in time solution or blow-up of any nonnegative solution, provided that the initial datum is nontrivial.
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