P. Quittner

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20152026

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math.AP2019

Entire and ancient solutions of a supercritical semilinear heat equation

Peter Poláčik, Pavol Quittner

We consider the semilinear heat equation $u_{t} = Δ u + u^{p}$ on $R^{N}$ . Assuming that $N \geq 3$ and $p$ is greater than the Sobolev critical exponent $(N + 2) / (N - 2)$ , we examine ent…

math.AP2019

On the multiplicity of self-similar solutions of the semilinear heat equation

Peter Poláčik, Pavol Quittner

In studies of superlinear parabolic equations \begin{equation*} u_t=Δu+u^p,\quad x\in {\mathbb R}^N,\ t>0, \end{equation*} where $p > 1$ , backward self-similar solutions play an impo…