Thresholds on growth of nonlinearities and singularity of initial functions for semilinear heat equations

Yasuhito Miyamoto, Masamitsu Suzuki

Let $N\ge 1$ and let $f\in C[0,\infty )$ be a nonnegative nondecreasing function and $u_0$ be a possibly singular nonnegative initial function. We are concerned with existence and n…