Determining Nodes for Semilinear Parabolic Evolution Equations in Banach Spaces

Autor:	Ryôhei Kakizawa
Rok vydání:	2019
Předmět:	Monomial Pure mathematics Partial differential equation Exponential convergence Applied Mathematics 010102 general mathematics Banach space 01 natural sciences 010101 applied mathematics Theoretical physics Initial value problem 0101 mathematics Finite set Equivalence (measure theory) Mathematics
Zdroj:	Acta Applicandae Mathematicae. 168:57-74
ISSN:	1572-9036 0167-8019
DOI:	10.1007/s10440-019-00279-9
Popis:	We are concerned with the determination of the asymptotic behavior of mild solutions to the abstract initial value problem for semilinear parabolic evolution equations in $L_{p}$ by the asymptotic behavior of these mild solutions on a finite set. More precisely, if the asymptotic behavior of the mild solution is known on an suitable finite set which is called determining nodes, then the asymptotic behavior of the mild solution itself is entirely determined. Not only the asymptotic equivalence but also the rate of monomial or exponential convergence can be clarified. We prove the above properties by the theory of analytic semigroups on Banach spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b5ba65c24da41afbc35c9b8a64a551a9 https://doi.org/10.1007/s10440-019-00279-9 Zobrazit plný text záznamu Full text from SpringerLink