This article is cited in 13 papers

Mixed problem for a higher-order nonlinear pseudoparabolic equation

T. K. Yuldashev^a, K. H. Shabadikov<sup>b

a</sup> M. F. Reshetnev Siberian State University of Science and Technologies
^b Ferghana State University

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.

Keywords: pseudoparabolic equation, generalized derivative, method of successive approximations, parameter, unique solvability.

UDC: 517.968

MSC: 35A02, 35M10, 35S05

 English version: Journal of Mathematical Sciences (New York), 2021, 254:6, 776–787

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