Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution

2025/07/14 by Andrea Dall’Aglio, Dall'Aglio, Andrea, Martina Magliocca +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2507.09978

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Logarithmic Sobolev Inequalities

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