Thresholds on growth of nonlinearities and singularity of initial functions for semilinear heat equations
Yasuhito Miyamoto,
Masamitsu Suzuki
Abstract:Let N ≥ 1 and let f ∈ C[0, ∞) be a nonnegative nondecreasing function and u 0 be a possibly singular nonnegative initial function. We are concerned with existence and nonexistence of a local in time nonnegative solution in a uniformly local Lebesgue space of a semilinear heat equationunder mild assumptions on f . A relationship between a growth of f and an integrability of u 0 is studied in detail. Our existence theorem gives a sharp integrability condition on u 0 in a critical and subcritical cases, and it ca… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.