QUASILINEAR DEGENERATE EVOLUTION EQUATIONS IN BANACH SPACES
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The quasilinear degenerate evolution equation of parabolic type <d(Mυ)>/<dt> +L(Mυ) υ=F(Mυ), 0< t≤ T considered in a Banach space X is written, putting Mv = u, in the from <du>/<dt>+A(υ) υ∍F(υ), 0< t ≤ T, where A(υ)=L(υ)M＾<−1> are multivalued linear operators in X for υ ∈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.
This is the author-created version of Springer, Journal of Evolution Equations, Vol.4, No.3, 2004, 421-449. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00028-004-0169-4
- Journal of Evolution Equations
Journal of Evolution Equations 4(3), 421-449, 2004-09
Birkhauser Verlag Basel