Conditions for the global solvability of an initial-boundary value problem for a nonlinear equation of pseudoparabolic typeстатья
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Аннотация:We consider the first boundary value problem for a nonlinear equation of pseudoparabolic type with the time derivative of a nonlinear elliptic operator. For small initial data, we prove solvability that is global over time. Under certain nonlinearity conditions, we prove solvability in any finite cylinder. Under other conditions in the case of large initial data, we prove the blow-up of the solution in finite time