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A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

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Abstract

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.

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Authors and Affiliations

  1. Institute of Cybernetics, National Academy of Sciences of Azerbaijan, ul. F. Agaeva 9, Baku, AZ1141, Azerbaijan

    I. G. Mamedov

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  1. I. G. Mamedov
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Correspondence to I. G. Mamedov.

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Original Russian Text © I.G. Mamedov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 1, pp. 99–110.

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Mamedov, I.G. A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation. Comput. Math. and Math. Phys. 49, 93–104 (2009). https://doi.org/10.1134/S0965542509010072

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  • DOI: https://doi.org/10.1134/S0965542509010072

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