ABSTRACT CAUCHY PROBLEMS FOR QUASI-LINEAR EVOLUTION EQUATIONS WITH NON-DENSELY DEFINED OPERATORS
| Autor: | Naoki Tanaka, Toshitaka Matsumoto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: |
Cauchy problem
Hille-Yosida operator General Mathematics 47J35 Linear operators Mathematical analysis Banach space 47H17 Cauchy distribution Type (model theory) abstract Cauchy problem 34G20 quasi-linear evolution equation Evolution equation comparison function mild solution Quasi linear Mathematics |
| Zdroj: | Taiwanese J. Math. 11, no. 2 (2007), 295-337 |
| Popis: | In this paper we study the abstract Cauchy problem for quasi-linear evolution equation $u'(t) = A(u(t)) u(t)$, where $\{ A(w); w \in W \}$ is a family of closed linear operators in a real Banach space $X$ such that $D(A(w)) = Y$ for $w \in W$, and $W$ is an open subset of another Banach space $Y$ which is continuously embedded in $X$. The purpose of this paper is not only to establish a ‘global’ well-posedness theorem without assuming that $Y$ is dense in $X$ but also to propose a new type of dissipativity condition which is closely related with the continuous dependence of solutions on initial data. |
| Databáze: | OpenAIRE |
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