The uniqueness class for the Cauchy problem for pseudoparabolic equations
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- by William Rundell PDF
- Proc. Amer. Math. Soc. 76 (1979), 253-257 Request permission
Abstract:
It is shown that the class of functions satisfying $|u(x,t)| \leqslant M{e^{\alpha |x|}}$ 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
- Robert Wayne Carroll and Ralph E. Showalter, Singular and degenerate Cauchy problems, Mathematics in Science and Engineering, Vol. 127, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460842
- William Rundell and Michael Stecher, The nonpositivity of solutions to pseudoparabolic equations, Proc. Amer. Math. Soc. 75 (1979), no. 2, 251–254. MR 532145, DOI 10.1090/S0002-9939-1979-0532145-9
- Tsuan Wu Ting, Parabolic and pseudo-parabolic partial differential equations, J. Math. Soc. Japan 21 (1969), 440–453. MR 264231, DOI 10.2969/jmsj/02130440
Additional Information
- © Copyright 1979 American Mathematical Society
- 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