A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid

We study the following initial-boundary value problem − + = , , ; , ; , where are given constants and and are given functions. In Part 1, we use the Galerkin method and compactness method to prove the existence of a unique weak solution of the problem above on for every In Part 2, we investigate asymptotic behavior of the solution as In Part 3, we prove the existence and uniqueness of a weak solution of problem − + = , , ; , associated with a “-periodic condition” , where is given constant.

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