Noncharacteristic mixed problems for hyperbolic systems of the first order

Ewa Zadrzyńska

GDML_Books, (1991), p.

Résumé

CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations of linear operators.............................................................................................................20 2.3. Properties of matrices..............................................................................................................................243. A boundary value problem for a linear hyperbolic system of the first order in a halfspace...........................26 3.1. Assumptions.............................................................................................................................................27 3.2. Construction of a symmetrizer..................................................................................................................31 3.3. An estimate of a solution of the boundary value problem (3.1)-(3.2) in $L²_{η}-norm$............................57 3.4. An estimate of a solution of the problem formally adjoint to (3.1)-(3.2) in $L²_{-η}-norm$.......................85 3.5. Existence and uniqueness of solution of the boundary value problem (3.1)-(3.2)....................................91 3.6. An estimate of a solution of the Cauchy problem for system (3.1) in $H^{s}_{η}$-norm...........................954. A mixed problem for a system of linear hyperbolic equations of the first order in a halfspace....................101 4.1. A mixed problem with nonzero initial condition........................................................................................101 4.2. A mixed problem with zero initial condition..............................................................................................1275. A mixed problem for a system of linear hyperbolic equations of the first order in a bounded domain.........1286. A mixed problem for a nonlinear system of hyperbolic equations of the first order.....................................141References....................................................................................................................................................145

1991 Mathematics Subject Classification: Primary 35L45, 35L50

Détail

Zbl 0763.35054

EUDML-ID : urn:eudml:doc:268579