| Author(s) |
Laurent Desvillettes ( )1, Klemens Fellner ()2, Michel Pierre ()3, Julien Vovelle ()3, 4 |
| Laboratory |
|
| Subject |
Mathematics/Numerical Analysis
|
| Title |
Global existence for quadratic systems of reaction-diffusion |
| Abstract |
We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of LlogL-entropy type holds. The approach relies on an a priori dimension-independent L-2-estimate, valid for a wider class of systems includingalso some classical Lotka-Volterra systems, and which provides an L-1-bound on the nonlinearities, at least for not too degenerate diffusions. In the more degenerate case, some global existence may be stated with the use of a weaker notion of renormalized solution with defect measure, arising in the theory of kinetic equations. |
| Fulltext language |
English |
|
| Journal |
advanced nonlinear studies |
| Audience |
international |
| Publication date |
2007 |
| Volume |
7 |
| Issue |
3 |
| Page, identifiant, ... |
491-511 |
|
| Keyword(s) |
reaction-diffusion system – Lotka-Volterra systems – weak solutions – renormalized solutions – global existence – entropy methods |
| Classification |
35K57 |
|
