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Three-dimensional nonlinear evolution equations of pseudoparabolic type in problems of mathematical physics. (Russian, English) Zbl 1121.35329
Zh. Vychisl. Mat. Mat. Fiz. 43, No. 12, 1835-1869 (2003); translation in Comput. Math. Math. Phys. 43, No. 12, 1765-1797 (2003).
Mathematical models of real-life three-dimensional processes, both dissipative and wave ones, are considered for certain problems of mathematical physics. It is shown that all these models are described by nonlinear evolutionary pseudoparabolic equations. In particular, some of these wave equations are model three-dimensional extensions of one-dimensional Benjamin-Bona-Mahony-Bürgers and Benjamin-Bona-Mahony equations, which describe surface waves in fluids.

35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction