Lp-maximal regularity for non-autonomous evolution equations
| Autor: | Wolfgang Arendt, César Poupaud, Ralph Chill, Simona Fornaro |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Cauchy problem
Non-autonomous Pure mathematics Applied Mathematics Operator (physics) 010102 general mathematics Mathematical analysis Nonlinear wave equation Banach space 01 natural sciences 010101 applied mathematics Nonlinear diffusion equation First order Cauchy problem Bounded function 0101 mathematics Lp-maximal regularity Second order Cauchy problem Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 237:1-26 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2007.02.010 |
| Popis: | Let A:[0,τ]→L(D,X) be strongly measurable and bounded, where D, X are Banach spaces such that D↪X. We assume that the operator A(t) has maximal regularity for all t∈[0,τ]. Then we show under some additional hypothesis (viz. relative continuity) that the non-autonomous problem(P)u˙+A(t)u=fa.e. on (0,τ),u(0)=x, is well-posed in Lp; i.e. for all f∈Lp(0,τ;X) and all x∈(X,D)1p∗,p there exists a unique u∈W1,p(0,τ;X)∩Lp(0,τ;D) solution of (P), where 1 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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