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Mixed Problem for a Higher-Order Nonlinear Pseudoparabolic Equation

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Abstract

We examine the unique generalized solvability of the mixed problem for a higher-order nonlinear pseudoparabolic equation with two parameters in mixed derivatives. Using the Fourier variable separation method, we reduce the problem to a countable system of nonlinear integral equations whose unique solvability can be proved by the method of successive approximations. We prove the continuous dependence of a generalized solution to the mixed problem on the initial functions and the positive parameters.

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Authors and Affiliations

  1. Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia

    T. K. Yuldashev

  2. Fergana State University, Fergana, Republic of Uzbekistan

    K. Kh. Shabadikov

Authors
  1. T. K. Yuldashev
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  2. K. Kh. Shabadikov
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Correspondence to T. K. Yuldashev.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 156, Mathematical Analysis, 2018.

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Yuldashev, T.K., Shabadikov, K.K. Mixed Problem for a Higher-Order Nonlinear Pseudoparabolic Equation. J Math Sci 254, 776–787 (2021). https://doi.org/10.1007/s10958-021-05339-w

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  • DOI: https://doi.org/10.1007/s10958-021-05339-w

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