About loss of regularity and "blow up" of solutions for quasilinear parabolic systems.
- Gajewski, Herbert
- Jäger, Willi
- Koshelev, Alexander
2010 Mathematics Subject Classification
- 35B65 35D10 35K40 35K57
- Parabolic systems, weak solutions, loss of regularity, chemotaxis system, semiconductor equations, numerical evidence
Starting from sufficient conditions for regularity of weak solutions to quasilinear parabolic systems, uecessary conditions for loss of regularity are formulated. It is shown numerically that in some situations loss of regularity ("blow up") really happens accordingly to these conditions.