Fujita exponent for heat equation with Hörmander vector fields
In this paper, we show global existence and non-existence results for the heat equation with sum of the squares of smooth vector fields on $$\mathbb {R}^{n}$$ satisfying Hörmander’s rank condition with a non-linearity of the form f(u), where f is a suitable function and u is the solution. In particular, when $$f(u)=u^p$$ , we calculate the critical Fujita exponent. We also give necessary conditions for blow-up or, alternatively, a sufficient condition for the existence of positive global solutions for time-dependent nonlinearities of the type $$\varphi (t)f(u)$$ .
Authors
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Aidyn Kassymov (ORCID: https://orcid.org/0000-0003-0080-4503)
- Marianna Chatzakou (ORCID: https://orcid.org/0000-0003-0853-3007)
Institutions
- Queen Mary University of London (GB)
- Ghent University (BE)
- Institute of Mathematics and Mathematical Modeling (KZ)
Publication Details
- Journal
- Annali di Matematica Pura ed Applicata (1923 -)
- Published
- 2026-04-17
- DOI
- https://doi.org/10.1007/s10231-026-01683-3
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- UK Research and Innovation
- Fonds Wetenschappelijk Onderzoek
- Universiteit Gent
- Vlaamse regering
- Engineering and Physical Sciences Research Council
- Bijzonder Onderzoeksfonds UGent