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Mixed Problem for a Nonlinear Parabolic Equation with Involution

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Abstract

In this paper, we consider a nonlinear parabolic differential equation with involution. With respect to spatial variable is used Dirichlet boundary value conditions and spectral problem with involution is obtained. Eigenvalues and eigenfunctions of the spectral problems are found. The Fourier series method of separation of variables is applied. The countable system of nonlinear integral equations is obtained. Theorem on a unique solvability of the countable system of nonlinear integral equations is proved. The method of successive approximations is used in combination with the method of contraction mapping. The generalized solution of the nonlinear mixed problem is obtained in the form of Fourier series. Absolutely and uniformly convergence of Fourier series is proved.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Tashkent State University of Economics, 100066, Tashkent, Uzbekistan

    T. K. Yuldashev

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  1. T. K. Yuldashev
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Correspondence to T. K. Yuldashev.

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Yuldashev, T.K. Mixed Problem for a Nonlinear Parabolic Equation with Involution. Lobachevskii J Math 44, 5519–5527 (2023). https://doi.org/10.1134/S1995080223120405

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