Stability in 𝐿𝑞-norm for inverse source parabolic problems

Author:

Melnig Elena-Alexandra1

Affiliation:

1. Faculty of Mathematics , University “Al. I. Cuza” , Iaşi , Romania ; and “Octav Mayer” Institute of Mathematics, Romanian Academy, Iaşi Branch

Abstract

Abstract We consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in L q {L^{q}} -norms, 2 q {2\leq q\leq\infty} , for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

Funder

Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Reference26 articles.

1. F. Ammar Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, Differ. Equ. Appl. 1 (2009), no. 3, 427–457.

2. F. Ammar Khodja, A. Benabdallah, C. Dupaix and I. Kostin, Controllability to the trajectories of phase-field models by one control force, SIAM J. Control Optim. 42 (2003), no. 5, 1661–1680.

3. V. Barbu, Exact controllability of the superlinear heat equation, Appl. Math. Optim. 42 (2000), no. 1, 73–89.

4. V. Barbu, Controllability of parabolic and Navier–Stokes equations, Sci. Math. Jpn. 56 (2002), no. 1, 143–211.

5. V. Barbu, The Carleman inequality for linear parabolic equations in LqL^{q}-norm, Differential Integral Equations 15 (2002), no. 5, 513–525.

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