A equação do calor com o operador de Grushin

Abstract

In this work, we study the heat equation with Grushin’s operator. We present an expression for its heat kernel and get regularity properties and decay on Lp spaces for both heat Kernel and semigroup associated to Grushin’s operator. Next, we use the results to prove the existence, uniqueness, continuous dependence and blowup alternative of mild solutions of a nonlinear Cauchy’s problem associated to Grushin’s operator.