| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 484, n. 2 APR 15 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider the linear Cauchy problem [u(t) = a(D)u, t is an element of R u(0) = u(0), (1) where a(D) : X -> X is a continuous linear operator on a Frechet space X. By imposing a condition (which is neither stronger nor weaker than the equicontinuity of the powers of a(D)), we present the necessary and sufficient conditions for the generation of a uniformly continuous group on X, which provides the unique solution of (1). In addition, for every pseudodifferential operator a(D) with constant coefficients defined on F L-loc(2), which is a Frechet space of distributions, we also provide the necessary and sufficient conditions such that the restriction [e(t) (a(D))](t >= 0) is a well defined semigroup on L-2 and E'. We conclude that the heat equation solution on F L-loc(2) for all t is an element of R extends the standard solution on Hilbert spaces for t >= 0. (C) 2019 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/02899-3 - Global solvability for differential complexes and converse to the theorem of the existence of Lyapunov function to gradient-like evolution process |
| Grantee: | Éder Ritis Aragão Costa |
| Support Opportunities: | Regular Research Grants |