QUASILINEAR DEGENERATE EVOLUTION EQUATIONS IN BANACH SPACES

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Abstract

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

  • Journal of Evolution Equations

    Journal of Evolution Equations 4(3), 421-449, 2004-09

    Birkhauser Verlag Basel

Codes

  • NII Article ID (NAID)
    120005285847
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    1424-3199
  • Data Source
    IR 
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