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- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Birkhäuser Verlag, Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-004-0169-4
- Publisher site
- See Article on Publisher Site
Abstract
The quasilinear degenerate evolution equation of parabolic type $$\frac{{d(Mv)}} {{dt}} + L(Mv)v = F(Mv),$$ 0< t ≤ T considered in a Banach space X is written, putting Mv = u , in the from $$\frac{{du}} {{dt}} + A(u)u \mathrel\backepsilon F(u),$$ 0< t ≤ T , where A ( u )= L ( u ) M −1 are multivalued linear operators in X for u ∈ K , K being a bounded ball || u || Z < R in another Banach space Z continuously embedded in X . Existence and uniqueness of the local solution for the related Cauchy problem are given. The results are applied to quasilinear elliptic-parabolic equations and systems.
Journal
Journal of Evolution Equations – Springer Journals
Published: Sep 1, 2004