Asymptotic behavior of solutions of pseudo-parabolic partial differential equations |
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Authors: | R. E. Showalter T. W. Ting |
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Affiliation: | (1) Urbana, Illinois, USA |
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Abstract: | 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. 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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