The nonlinear heat equation involving highly singular initial values and new blowup and life span results

Slim Tayachi, Fred B. Weissler

In this paper we prove local existence of solutions to the nonlinear heat equation $u_t = Δu +a |u|^αu, \; t\in(0,T),\; x=(x_1,\,\cdots,\, x_N)\in {\mathbb R}^N,\; a = \pm 1,\; α>0…