Abstract
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 toC2+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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