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This article is cited in 3 scientific papers (total in 3 papers)
Weak solutions of linear equations of Sobolev type and semigroups of operators
V. E. Fedorov Chelyabinsk State University
Abstract:
We show that there is an infinitely differentiable semigroup for the equation $L\dot u=Mu$
if the $(p,\psi(\tau))$-condition introduced in this paper holds for the pair of operators $(L,M)$.
In the case when the strong $(p,\psi(\tau))$-condition holds we have found the set of one-valued solubility of the weakened Cauchy problem for this equation. Our results supplement the theory of degenerate semigroups of operators and generalize in part the theorem on the generators of semigroups of class $(A)_\infty$ to the case of degenerate semigroups. We investigate the kernels and images of the semigroups constructed and consider various examples of operators for which the $(p,\psi(\tau))$-condition (the strong $(p,\psi(\tau))$-condition) holds.
Received: 06.03.2000
Citation:
V. E. Fedorov, “Weak solutions of linear equations of Sobolev type and semigroups of operators”, Izv. RAN. Ser. Mat., 67:4 (2003), 171–188; Izv. Math., 67:4 (2003), 797–813
Linking options:
https://www.mathnet.ru/eng/im445https://doi.org/10.1070/IM2003v067n04ABEH000445 https://www.mathnet.ru/eng/im/v67/i4/p171
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Abstract page: | 437 | Russian version PDF: | 222 | English version PDF: | 21 | References: | 46 | First page: | 1 |
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