Mixed Problem for a Higher-Order Nonlinear Pseudoparabolic Equation

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 so...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 254; no. 6; pp. 776 - 787
Main Authors Yuldashev, T. K., Shabadikov, K. Kh
Format Journal Article
LanguageEnglish
Published New York Springer US 02.05.2021
Springer
Springer Nature B.V
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-021-05339-w

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Summary: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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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05339-w