Weakly Hyberbolic Equations in Domains with Boundaries

D'Ancona, Piero; Racke, Reinhard

Weakly Hyberbolic Equations in Domains with Boundaries

Dateien

preprint_022.pdfGröße: 282.57 KBDownloads: 84

Datum

1996

Autor:innen

D'Ancona, Piero

Racke, Reinhard

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

We consider weakly hyperbolic equations of the type utt(t)+a(t)Au(t)=f(t,u(t)), u(0)=u0, ut(0)=u1, u(t) in D(A), t in [0,T], for a function u:[0,T]->H, T a nonnegative real, H a separable Hilbert space, A being a non-negative, self-adjoint operator with domain D(A). The real function a is assumed to be non-negative, continuous and (piecewise) continuous differentiable, and the derivative a' will have to satisfy an integrability condition, which will admit infinitely many oscillations near the point of degeneration. For given initial data u0, u1 a global existence theorem in C([0,T],D(As)) is proved for the linear problem f=f(t). If a' does not change sign, the result can be improved, and finally a local (in time) existence theorem can be proved for nonlinearities f essentially satisfying the mapping property f(., D(As)) is subset of D(As), where s>0 describes the regularity class. In the applications, A will be a uniformly elliptic operator in a domain Omega, Omega being a bounded domain with smooth boundary in Rn, n>=2, for second-order operators then describing a weakly hyperbolic wave equation.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

D'ANCONA, Piero, Reinhard RACKE, 1996. Weakly Hyberbolic Equations in Domains with Boundaries

BibTex

@unpublished{DAncona1996Weakl-710,
  year={1996},
  title={Weakly Hyberbolic Equations in Domains with Boundaries},
  author={D'Ancona, Piero and Racke, Reinhard}
}

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