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Perturbation Method for First- and Complete Second-Order Differential Equations

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Abstract

We are concerned with an inverse problem for a linear evolution equation of the first order. Both hyperbolic and parabolic cases will be considered. A complete second-order evolution equation will be considered together with a related identification problem. We indicate sufficient conditions for the existence and the uniqueness of a solution to these problems. All the results apply well to inverse problems for equations from mathematical physics. Indeed, as a possible application of the abstract theorems, some examples of partial differential equations are given.

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Author notes

  1. Mohammed Al Horani

    Present address: Department of Mathematics, Faculty of Science, University of Hail, Ha‘il, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics, The University of Jordan (Sabbatical Year), Amman, Jordan

    Mohammed Al Horani

  2. Dipartimento Di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    Angelo Favini

Authors
  1. Mohammed Al Horani
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  2. Angelo Favini
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Correspondence to Angelo Favini.

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Al Horani, M., Favini, A. Perturbation Method for First- and Complete Second-Order Differential Equations. J Optim Theory Appl 166, 949–967 (2015). https://doi.org/10.1007/s10957-015-0733-9

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  • DOI: https://doi.org/10.1007/s10957-015-0733-9

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