The Optimal Stability Estimate for some Ill-posed Cauchy Problems for a Parabolic Equation

Knabner P, Vessella S (1988)

Publication Language: English

Publication Type: Journal article

Publication year: 1988

Journal

Mathematical Methods in the Applied Sciences Wiley

Book Volume: 10

Pages Range: 575-583

Journal Issue: 5

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_1988/1988_KnVessella_TheOptimStabilEstimForSomeIllposedCauchyProblForAParabolEquation

DOI: 10.1002/mma.1670100507

Abstract

In this paper we consider the non‐characteristic Cauchy problem u_t−a(x)u_xx−b(x)u_x−c(x)u = 0, x ∈ (0, l), t ∈ I, u(0, t) = φ(t), u_x(0, t) = 0, t ∈ I, where I = ℝ or I = ℝ⁺ and u(x, 0) = 0, x ∈ [0, l], in the case I = ℝ⁺. Assuming an a priori bound for ‖u(l,.)‖ urn:x-wiley:01704214:media:MMA1670100507:tex2gif-inf-5 , we derive the exact Hölder type dependence of on ‖u(x,.)‖ on ‖φ‖.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Knabner, P., & Vessella, S. (1988). The Optimal Stability Estimate for some Ill-posed Cauchy Problems for a Parabolic Equation. Mathematical Methods in the Applied Sciences, 10(5), 575-583. https://dx.doi.org/10.1002/mma.1670100507

MLA:

Knabner, Peter, and Sergio Vessella. "The Optimal Stability Estimate for some Ill-posed Cauchy Problems for a Parabolic Equation." Mathematical Methods in the Applied Sciences 10.5 (1988): 575-583.

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