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math.AP2024
A non-linear characterization of stochastic completeness of graphs
Marcel Schmidt, Ian Zimmermann
We study non-linear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion…
math.AP2021
Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source
Daniel Lenz, Marcel Schmidt, Ian Zimmermann
We give a sufficient condition for non-existence of global nonnegative mild solutions of the Cauchy problem for the semilinear heat equation in for $p \…