The Cauchy problem in Hölder spaces for heat conductivity equations with essentially variable coefficient (Q2719457)

The authors study the Cauchy problem for heat conductivity equation in the case when the the heat conductivity coefficient is varying essentially. It is assumed that this variation is characterized by the weight function \(\alpha(x)\), \(x\in\mathbb R_1\), and \(\alpha(x)>0\) for all \(x\in \mathbb R\backslash\{0\}\), and the function \(\frac{1}{\alpha(x)}\) has an integral singularity at point \(x=0\). At infinity the function \(\frac{1}{\alpha(x)}\) has a nonintegrable singularity. The main result of the paper is a theorem on existence and uniqueness of solutions of the problem in Hölder spaces.