Work

Diffusion bounds for non-autonomous degenerate parabolic equations

Year: 2026

Type: preprint

Abstract: We consider possibly degenerate non-autonomous parabolic equations in $L^p$ spaces for all $1\le p\le\infty$, and prove Gaussian space-time upper bounds of the Davies-Gaffney, or integrated Nash-Aronson, type on their solutions. Our bounds cover both linear and nonlinear equations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.19540

Authors: Lemm, Marius, Sigal, Israel Michael, Zhang, Jingxuan

Institution: University of Tübingen

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, China Postdoctoral Science Foundation, Tsinghua University, Natural Sciences and Engineering Research Council of Canada

Awards: G2336692412, G2650887284, G5141357660, TRR 352: Mathematik der VielteilchenQuantensysteme und ihrer kollektiven Phänomene

OpenAlex ID: W7140101446

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