Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution
Analysis of PDEs
2025-07-15 v1
Abstract
In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two different situations are analyzed. On the one hand, we assume that the initial datum belongs to an Orlicz space of exponentially summable functions. On the other, data in an appropriate Lebesgue space satisfying a smallness condition are considered. Our results are coherent with those of previous papers in similar frameworks.
Keywords
Cite
@article{arxiv.2507.09978,
title = {Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution},
author = {Andrea Dall'Aglio and Martina Magliocca and Sergio Segura de León},
journal= {arXiv preprint arXiv:2507.09978},
year = {2025}
}