Abstract
In this paper, we construct the conditions for the existence of a degenerate nonlinear resolving semigroup of shift operators for a semilinear Sobolev type equation. Based on the phase space method, we find the conditions for the existence of solutions to the Cauchy problem for a semilinear Sobolev type equation. The solutions are defined only on a simple Banach manifold (quasistationary trajectories). Also, we find the conditions under which the solution can be continued in time. The obtained abstract results are illustrated by the Cauchy–Dirichlet problem for the generalized filtration Boussinesq equation.
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V. Vasiuchkova, K., Manakova, N.A., Sviridyuk, G.A. (2020). Degenerate Nonlinear Semigroups of Operators and Their Applications. In: Banasiak, J., Bobrowski, A., Lachowicz, M., Tomilov, Y. (eds) Semigroups of Operators – Theory and Applications. SOTA 2018. Springer Proceedings in Mathematics & Statistics, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-030-46079-2_21
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