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Proceedings of the American Mathematical Society

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The uniqueness class for the Cauchy problem for pseudoparabolic equations


Author: William Rundell
Journal: Proc. Amer. Math. Soc. 76 (1979), 253-257
MSC: Primary 35K30
DOI: https://doi.org/10.1090/S0002-9939-1979-0537083-3
MathSciNet review: 537083
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Abstract: It is shown that the class of functions satisfying $ \vert u(x,t)\vert \leqslant M{e^{\alpha \vert x\vert}}$ forms a uniqueness class for the Cauchy problem for pseudoparabolic equations. The surprising fact is that, unlike the case of parabolic equations, the constant $ \alpha $ is not arbitrary but depends on the coefficients of the equation.


References [Enhancements On Off] (What's this?)

  • [1] R. W. Carroll and R. E. Showalter, Singular and degenerate Cauchy problems, Academic Press, New York, 1976. MR 0460842 (57:834)
  • [2] W. Rundell and M. Stecher, The nonpositivity of solutions to pseudoparabolic equations, Proc. Amer. Math. Soc.75 (1979), 251-254. MR 532145 (80e:35031)
  • [3] T. W. Ting, Parabolic and pseudoparabolic differential equations, J. Math. Soc. Japan 21 (1969), 440-453. MR 0264231 (41:8827)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0537083-3
Article copyright: © Copyright 1979 American Mathematical Society

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