Mixed Grushin Heat Equations with Riesz-Potential Nonlinearities in Marcinkiewicz Spaces: Subcritical, Critical, and Supercritical Regimes
Year: 2026
Type: preprint
Abstract: We study the nonlinear evolution equation $$ \partial_t u+(G+G^δ)u=I_α(|u|^ρ) \quad\text{on }\mathbb{R}^{N+k}, $$ where $G$ is the nonnegative self adjoint realization of Grushin operator, $0<δ<1$, and $I_α$ is the potential operator with kernel $|z|^{-α}$, $0<α1+p/β$, well-posedness is recovered in higher-integrability Marcinkiewicz spaces $L^{q,\infty}$ satisfying $$ β(ρ-1)
Source: arXiv (Cornell University)
Authors: Dasgupta, Aparajita, Dolai, Uttam Kumar
Institution: Indian Institute of Technology Delhi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214014308