Semigroups of operators and second-order Cauchy problems (Q762445)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Semigroups of operators and second-order Cauchy problems |
scientific article; zbMATH DE number 3888385
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semigroups of operators and second-order Cauchy problems |
scientific article; zbMATH DE number 3888385 |
Statements
Semigroups of operators and second-order Cauchy problems (English)
0 references
1985
0 references
Let A be the infinitesimal generator of a semigroup \(\{\) T(t)\(\}\) of operators in a Banach space X. Conditions are given which imply that \(u(t)=T(t)x\) is the only solution of the Cauchy problem \(u''(t)=A^ 2u(t),\quad u(0)=x\) that satisfies one of the conditions \(u(\infty -)=0\) or \(u(t)=O(1)\) at \(\infty\).
0 references
second-order Cauchy problems
0 references
infinitesimal generator of a
0 references
semigroup of operators in a Banach space
0 references
