Fundamental Solution of the Cauchy Problem for \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \)-Parabolic Systems with Variable Coefficients

Abstract

We define a class of parabolic systems of partial differential equations and substantiate their \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \) -parabolicity. We study the properties of the spatial behavior of fundamental solutions of the Cauchy problem for \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \) -parabolic systems with time-dependent coefficients and present examples of these systems.