Details
| Original language | English |
|---|---|
| Pages (from-to) | 283-317 |
| Number of pages | 35 |
| Journal | Journal of differential equations |
| Volume | 429 |
| Early online date | 19 Feb 2025 |
| Publication status | E-pub ahead of print - 19 Feb 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.
Keywords
- Atmospheric flows, Critical spaces, Quasilinear parabolic equations, Scaling invariance, Semilinear parabolic equations
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of differential equations, Vol. 429, 05.06.2025, p. 283-317.
Research output: Contribution to journal › Article › Research › 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 - 2025/2/19
Y1 - 2025/2/19
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 -