Uniqueness and norm convexity in the Cauchy problem for evolution equations with convolution operators
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- by Monty J. Strauss
- Proc. Amer. Math. Soc. 35 (1972), 423-430
- DOI: https://doi.org/10.1090/S0002-9939-1972-0310478-2
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Abstract:
Uniqueness in the Cauchy problem is shown under suitable conditions for evolution equations of the form ${u_t}(x,t) - B(t,{D_x})u(x,t) = 0$ , where B is a pseudo-differential operator of order $k \geqq 0$ in the x variables. This is proved as a corollary to a norm convexity relation. In the process of showing this, an extension to Hölder’s inequality is derived.References
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Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 423-430
- MSC: Primary 35S10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0310478-2
- MathSciNet review: 0310478