Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_t-\Delta u=|u{|}^{\alpha }u$ on ${\mathbb{R}}^N$, where $\alpha >0$ and $N\ge 1$. We prove that in the range $0<\alpha <\frac{4}{N-2}$, for every $\mu >0$, there…