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Blow‐up regions for a class of fractional evolution equations with smoothed quadratic nonlinearities.
- Source :
- Mathematische Nachrichten; Aug2022, Vol. 295 Issue 8, p1462-1479, 18p
- Publication Year :
- 2022
-
Abstract
- We consider an n‐dimensional parabolic‐type PDE with a diffusion given by a fractional Laplace operator and with a quadratic nonlinearity of the "gradient" of the solution, convoluted with a term b$\mathfrak {b}$ which can be singular. Our first result is the well‐posedness for this problem: We show existence and uniqueness of a (local in time) mild solution. The main result is about blow‐up of said solution, and in particular we find sufficient conditions on the initial datum and on the term b$\mathfrak {b}$ to ensure blow‐up of the solution in finite time. [ABSTRACT FROM AUTHOR]
- Subjects :
- EVOLUTION equations
QUADRATIC equations
BLOWING up (Algebraic geometry)
Subjects
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 295
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 158751522
- Full Text :
- https://doi.org/10.1002/mana.202000480