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Global behavior of solutions to an inverse problem for semilinear hyperbolic equations

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Abstract

This paper is concerned with global in time behavior of solutions for a semilinear, hyperbolic, inverse source problem. We prove two types of results. The first one is a global nonexistence result for smooth solutions when the data is chosen appropriately. The second type of results is the asymptotic stability of solutions when the integral constraint vanishes as t goes to infinity. Bibliography: 22 titles.

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Authors and Affiliations

  1. Department of Mathematics, Bogazici University, Istanbul, Turkey

    A. Eden

  2. Department of Mathematics, Koç University, Istanbul, Turkey

    V. K. Kalantarov

Authors
  1. A. Eden
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  2. V. K. Kalantarov
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Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 120–134.

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Eden, A., Kalantarov, V.K. Global behavior of solutions to an inverse problem for semilinear hyperbolic equations. J Math Sci 136, 3718–3727 (2006). https://doi.org/10.1007/s10958-006-0195-6

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  • DOI: https://doi.org/10.1007/s10958-006-0195-6

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