Summary
Consider a solution to a second-order pseudo-parabolic equation with sufficiently smooth time-independent coefficients in a cylindrical domain. If it vanishes on the cylindrical surface for all times and if its restriction to a fixed instant belongs toC 2+a , then its pointwise values decay exponentially as t→∞ while its Dirichlet norm grows expontially as t→−∞. Similar conclusion still hold for solutions to non-homogeneous equations under non-homogeneous boundary conditions provided the free term and the boundary data posses these asymptotic behaviors.
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Work of the second named author was partially supported by N.S.F. Grant No. GP-19590.
Entrata in Redazione il 29 gennaio 1971.
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Showalter, R.E., Ting, T.W. Asymptotic behavior of solutions of pseudo-parabolic partial differential equations. Annali di Matematica 90, 241–258 (1971). https://doi.org/10.1007/BF02415050
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DOI: https://doi.org/10.1007/BF02415050