Stability of a semilinear Cauchy problem (Q2759785)

This paper discusses the stability and instability of positive radial steady states of the following Cauchy problem: NEWLINE\[NEWLINE{\partial u \over \partial t }= \Delta u + K (|x|)u^p \quad\text{in }\mathbb{R} \times (0,T),\qquad u(x,0) = \varphi(x)\quad\text{in }\mathbb{R},NEWLINE\]NEWLINE where \( p>1\). The authors introduce an estimate on the solution and asymptotic expansions of solutions, then prove the stability and asymptotic stability of the steady state of this problem.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].