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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 23, Issue 1


Stability estimates for Burgers-type equations backward in time

Dinh Nho Hào / Nguyen Van Duc / Nguyen Van Thang
Published Online: 2014-04-18 | DOI: https://doi.org/10.1515/jiip-2013-0050


We prove stability estimates of Hölder-type for Burgers-type equations ut = (a(x,t)ux)x - d(x,t)uux + f(x,t), (x,t) ∈ (0,1)×(0,T), u(0,t) = g0(t), u(1,t) = g1(t), 0 ≤ tT, backward in time, with a(x,t), d(x,t), g0(t), g1(t), f(x,t) being smooth functions, under relatively weak conditions on the solutions.

Keywords: Burgers-type equations backward in time; stability estimates; log-convexity method; nonlinear ill-posed problems

MSC: 65N20; 65N21; 47J06

About the article

Received: 2013-08-29

Revised: 2014-03-11

Accepted: 2014-03-12

Published Online: 2014-04-18

Published in Print: 2015-02-01

Funding Source: Vietnam National Foundation for Science and Technology Development (NAFOSTED)

Award identifier / Grant number: 101.02-2011.50

Funding Source: Vietnam Ministry of Education and Training

Award identifier / Grant number: B2013-27-09

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 1, Pages 41–49, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2013-0050.

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