Stabilization of Ill-Posed Cauchy Problems for Parabolic Equations

Knabner P, Vessella S (1987)

Publication Language: English

Publication Type: Journal article

Publication year: 1987

Journal

Annali Di Matematica Pura Ed Applicata Springer Verlag (Germany)

Book Volume: 149

Pages Range: 393-409

Journal Issue: 1

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_1987/1987_KnVessella_StabilizationOfIllPosedCauchyProblemsForParaEquation

DOI: 10.1007/BF01773944

Abstract

In this paper we study the noncharacteristic Cauchy problem, u_t−(a(x)u_x)_x=0, x∈(0, l), t∈.(0, T], u(0, t)=ϕ(t), u_x(0,t)=0, 0≦t≦T, assuming only L^∞ for a. In the case of weak a priori bounds on u, we derive stability estimates on u of Hölder type in the interior and of logarithmic type at the boundary. Also the continuous dependence on a is considered.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Knabner, P., & Vessella, S. (1987). Stabilization of Ill-Posed Cauchy Problems for Parabolic Equations. Annali Di Matematica Pura Ed Applicata, 149(1), 393-409. https://doi.org/10.1007/BF01773944

MLA:

Knabner, Peter, and Sergio Vessella. "Stabilization of Ill-Posed Cauchy Problems for Parabolic Equations." Annali Di Matematica Pura Ed Applicata 149.1 (1987): 393-409.

BibTeX: Download