Quasilinear parabolic problems via maximal regularity

By Herbert Amann. Advances in Differential Equations, 2005

63 citations recorded by the source corpus.

We use maximal Lp regularity to study quasilinear parabolic evolution equations. In contrast to all previous work we only assume that the nonlinearities are defined on the space in which the solution is sought for. It is shown that there exists a unique maximal solution depending continuously on all data, and criteria for global existence are given as well. These general results possess numerous applications, some of which will be discussed in separate publications.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/606e8f5c8326596d6b07cdd101b2d8a3de865bd5

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In Applied Mathematics

1. M. Wilke
2. Matthias Köhne
3. Jan Prüss
4. Mark Veraar
5. M. Meyries
6. C. Gallarati
7. Matthias Kotschote
8. Jan Pruess

In Control and Systems Engineering

1. M. Wilke
2. Jan Prüss
3. Matthias Köhne
4. Mark Veraar
5. C. Gallarati
6. Jan Pruess

In Mathematical Physics

1. M. Wilke
2. Matthias Köhne
3. Jan Prüss
4. M. Meyries
5. Roland Schnaubelt

Citations in the corpus

• On quasilinear parabolic evolution equations in weighted Lp-spaces (2009, methodology): “ stability of equilibria, invariant manifolds near equilibria, and asymptotic behaviour of the solutions, especially their convergence to an equilibrium. There are numerous contributions to this field [1, 2, 3, 4, 5, 10, 11, 14, 18, 22, 28, 29, 30, 32]; this is just a selection. Here we follow the ap”