On the Heat equation involving a Grushin operator in Marcinkiewcz spaces

2025/01/09 by Kogoj, Alessia E., Lima, Maria E., Viana, Arlúcio · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.04909

Abstract

In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator Δ_G=\dfrac12(Δ_x+|x|²Δ_y) in Marcinkiewicz spaces. Furthermore, we provide sufficient conditions for the existence of positive, symmetric, and self-similar solutions.

Cited by

• Nonexistence of global solutions to the Grushin heat equation with nonlocal and local nonlinearities
• Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
• Local and global solvability of the Grushin heat equation with mixed nonlinear memory and reaction terms

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