Abstract Cauchy problems for quasilinear operators whose domains are not necessarily dense or constant
| Autor: | Naoki Tanaka, Toshitaka Matsumoto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Cauchy problem
Discrete mathematics Applied Mathematics 010102 general mathematics 05 social sciences Linear operators Banach space Cauchy distribution Projection operator 01 natural sciences Abstract Cauchy problems for quasilinear operators 0502 economics and business Evolution equation Nondense domain Initial value problem Uniqueness 0101 mathematics Constant (mathematics) 050203 business & management Analysis Mathematics |
| Zdroj: | Nonlinear Analysis. 162:91-112 |
| ISSN: | 0362-546X |
| Popis: | The solvability of the abstract Cauchy problem for the quasilinear evolution equation u ′ ( t ) = A ( u ( t ) ) u ( t ) for t > 0 and u ( 0 ) = u 0 ∈ D is discussed. Here { A ( w ) ; w ∈ Y } is a family of closed linear operators in a real Banach space X such that Y ⊂ D ( A ( w ) ) ⊂ Y ¯ for w ∈ Y , Y is another Banach space which is continuously embedded in X , and D is a closed subset of Y . The existence and uniqueness of C 1 solutions to the Cauchy problem is proved without assuming that Y is dense in X or D ( A ( w ) ) is independent of w . The abstract result is applied to obtain an L 1 -valued C 1 -solution to a size-structured population model. |
| Databáze: | OpenAIRE |
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