Strongly compatible generators of groups on Frechet spaces

Autor(es)

Aragao-Costa, E. R. ^[1] ; da Silva, A. P. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 484, n. 2 APR 15 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/02899-3 - Resolubilidade global para complexos diferenciais e recíproca para o teorema de existência de função de Lyapunov não autônoma para processos de evolução de tipo gradiente
• Beneficiário: Éder Ritis Aragão Costa
• Modalidade de apoio: Auxílio à Pesquisa - Regular