Matioc, Bogdan-Vasile and Roberti, Luigi and Walker, Christoph (2025) Quasilinear parabolic equations with superlinear nonlinearities in critical spaces. JOURNAL OF DIFFERENTIAL EQUATIONS, 429. pp. 283-317. ISSN 0022-0396, 1090-2732
Full text not available from this repository. (Request a copy)Abstract
Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations ut = A(u)u + f (u) is established in a certain critical case of strict inclusion dom(f ) dom(A) for the domains of the (superlinear) function u -> f (u) and the quasilinear part u -> A(u). Based upon regularizing effects of parabolic equations, it is proven that the solution map generates a semiflow in a critical intermediate space. The applicability of the abstract results is demonstrated by several examples including a model for atmospheric flows and semilinear and quasilinear evolution equations with scaling invariance for which well-posedness in the critical scaling invariant intermediate spaces is shown. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EVOLUTION-EQUATIONS; GLOBAL-SOLUTIONS; WELL-POSEDNESS; STABILITY; Quasilinear parabolic equations; Semilinear parabolic equations; Critical spaces; Scaling invariance; Atmospheric flows |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Jun 2026 05:58 |
| Last Modified: | 18 Jun 2026 05:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66995 |
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