Author | Caps, Oliver. author |
---|---|
Title | Evolution Equations in Scales of Banach Spaces [electronic resource] / by Oliver Caps |
Imprint | Wiesbaden : Vieweg+Teubner Verlag, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-322-80039-8 |
Descript | 309 p. 2 illus. online resource |
1 Tools from functional analysis -- 1.1 A brief introduction into the theory of semigroups -- 1.2 Selfadjoint operators -- 1.3 Generators of analytic semigroups and their powers -- 1.4 Fractional Powers of operators of positive type -- 1.5 Complex interpolation spaces -- 1.6 Time-dependent, linear evolution equations -- 2 Well-posedness of the time-dependent linear Cauchy problem -- 2.1 Properties of well-posed linear Cauchy problems in scales of Banach spaces -- 2.2 Scales of Banach spaces generated by families of closed operators -- 2.3 Commutator estimates and scales of Banach spaces -- 2.4 Characterization of well-posedness of the Cauchy problem.. -- 2.5 Sufficient conditions for well-posedness of the Cauchy problem -- 3 Quasilinear Evolution Equations -- 3.1 Semilinear Evolution Equations -- 3.2 Commutator estimates and quasilinear evolution equations -- 3.3 A local existence and uniqueness result for quasilinear evolution equations -- 3.4 Regularity for quasilinear evolution equations in scales of Banach spaces -- 4 Applications to linear, time-dependent evolution equations -- 4.1 Pseudodifferential operators and weighted Sobolev spaces -- 4.2 Pseudodifferential evolution equations in scales of weighted Sobolev spaces -- 4.3 Essential selfadjointness of pseudodifferential operators -- 4.4 Evolution equations in C0(IRn) and Feller semigroups -- 4.5 Evolution equations in scales of Lq-Sobolev spaces -- 4.6 An application to a degenerate-elliptic boundary value problem -- 4.7 Evolution equations on networks -- 5 Applications to quasilinear evolution equations -- 5.1 Estimates of Nash-Moser type for differential operators -- 5.2 Quasilinear evolution equations in Sobolev spaces -- 5.3 Degenerate Navier-Stokes equations -- 5.4 The generalized Kadomtsev-Petviashvili equation -- 5.5 Quasilinear evolution equations in scales of Lq-Sobolev spaces -- 5.6 First order hyperbolic evolution equations in the C0k-scale