The Cauchy--Dirichlet problem for the heat equation in Besov spaces

E. Zadrzyńska ; W. Zajączkowski

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 40-97

Résumé

In the paper, we study the solvability in anisotropic spaces $B_{p,q}^{{\sigma\over2}\!,\sigma}(\Omega^T)$, $\sigma\in\mathbb R_+$, $p,q\in(1,\infty)$, of the heat equation $u_t-\Delta u=f$ in $\Omega^T\equiv(0,T)\times\Omega$ with the boundary and initial conditions: $u=g$ on $S^T$, $u|_{t=0}=u_0$ in $\Omega$, where $S$ is the boundary of a bounded domain $\Omega\subset\mathbb R^n$.