On the Heat equation involving a Grushin operator in Marcinkiewcz spaces

Abstract

In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator $${\Delta }_{\mathcal{G}}=\frac{1}{2}\left({\Delta }_x+|x{|}^2{\Delta }_y\right)$$ in Marcinkiewicz spaces. Furthermore, we provide sufficient conditions for the existence of positive, symmetric, and self-similar solutions.

To appear in "Revista Matemática Complutense"