Space analyticity for the nonlinear heat equation in a bounded domain (Q1288861)

The authors provide an estimate of the analyticity radius of the solution to the following nonlinear heat equation \[ \partial_t u-\Delta u=u^k,\quad t>0,\qquad u\big| _{\partial \Omega}=0,\quad t>0,\qquad u(x,0)=u_0(x), \quad x\in\Omega, \] where \(k\in \{2,3,\ldots\},\) \(\Omega\subset \mathbb{R}^D\) is a bounded domain with a smooth boundary and \(u_0\in L^{2p}(\Omega)\) with \(2p\in [2,+\infty).\)