The semilinear heat equation $u' = Lu + f(u)$, where $L$ is a Laplacian, has been studied on manifolds and metric measure spaces and, more recently, on graphs. Under the assumption that $f$ is convex, we give a sufficient condition for blow-up of nonnegative solutions of this equation in the setting of Lebesgue spaces over an abstract measure space. Our work recovers and extends some blow-up results from the three separate contexts mentioned above in a unified framework. The talk is based on joint work with Daniel Lenz and Marcel Schmidt.

9.23海报.pdf