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

  • I. G. Mamedov
Article

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.

Keywords

fourth-order pseudoparabolic equation Cauchy problem equations with discontinuous coefficients fundamental solution 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of CyberneticsNational Academy of Sciences of AzerbaijanBakuAzerbaijan

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