Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 283-317 |
| Seitenumfang | 35 |
| Fachzeitschrift | Journal of differential equations |
| Jahrgang | 429 |
| Frühes Online-Datum | 19 Feb. 2025 |
| Publikationsstatus | Veröffentlicht - 5 Juni 2025 |
Abstract
Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations u′=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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Journal of differential equations, Jahrgang 429, 05.06.2025, S. 283-317.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Quasilinear parabolic equations with superlinear nonlinearities in critical spaces
AU - Matioc, Bogdan Vasile
AU - Roberti, Luigi
AU - Walker, Christoph
N1 - Publisher Copyright: © 2025 The Author(s)
PY - 2025/6/5
Y1 - 2025/6/5
N2 - Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations u′=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.
AB - Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations u′=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.
KW - Atmospheric flows
KW - Critical spaces
KW - Quasilinear parabolic equations
KW - Scaling invariance
KW - Semilinear parabolic equations
UR - http://www.scopus.com/inward/record.url?scp=85217975394&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2025.02.039
DO - 10.1016/j.jde.2025.02.039
M3 - Article
AN - SCOPUS:85217975394
VL - 429
SP - 283
EP - 317
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
ER -