Rocky Mountain Journal of Mathematics

On a solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions

Stevan Pilipović, Bojan Prangoski, and Daniel Velinov

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Results of Da Prato and Sinestrari \cite {d81} on differential operators with non-dense domain but satisfying the Hille-Yosida condition, are applied in the setting of Beurling weighted spaces of ultradistributions $\DD '^{(s)}_{L^p}((0,T)\times U)$, where $U$ is open and bounded set in $\mathbb R^d$. For this purpose, the new structural theorems were given for $\DD '^{(s)}_{L^p}((0,T)\times U)$. Then a class of the Cauchy problems in the general setting of such spaces of ultradistributions is analyzed.

Article information

Rocky Mountain J. Math., Volume 45, Number 6 (2015), 1937-1984.

First available in Project Euclid: 14 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
Secondary: 35A01: Existence problems: global existence, local existence, non-existence

Cauchy problem strict weak solution $F$-weak solution


Pilipović, Stevan; Prangoski, Bojan; Velinov, Daniel. On a solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions. Rocky Mountain J. Math. 45 (2015), no. 6, 1937--1984. doi:10.1216/RMJ-2015-45-6-1937.

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