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

Author

Listed:
  • Mohammed Al Horani

    (The University of Jordan (Sabbatical Year)
    University of Hail)

  • Angelo Favini

    (Universita di Bologna)

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.

Suggested Citation

  • Mohammed Al Horani & Angelo Favini, 2015. "Perturbation Method for First- and Complete Second-Order Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 949-967, September.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-015-0733-9
    DOI: 10.1007/s10957-015-0733-9
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    References listed on IDEAS

    as
    1. A. Favini & G. Marinoschi, 2010. "Identification of the Time Derivative Coefficient in a Fast Diffusion Degenerate Equation," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 249-269, May.
    2. M. AL Horani & A. Favini, 2006. "An Identification Problem for First-Order Degenerate Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 41-60, July.
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    Cited by:

    1. Shangquan Bu & Gang Cai, 2023. "Periodic solutions of second‐order degenerate differential equations with infinite delay in Banach spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2276-2292, June.

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