Stability for non-autonomous linear evolution equations with L p -maximal regularity

Hafida Laasri; Omar El-Mennaoui

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 4, page 887-908
  • ISSN: 0011-4642

Abstract

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We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem ( P ) u ˙ ( t ) + A ( t ) u ( t ) = f ( t ) t -a.e. on [ 0 , τ ] , u ( 0 ) = 0 , where A : [ 0 , τ ] → ℒ ( X , D ) is a bounded and strongly measurable function and X , D are Banach spaces such that D → d ↪ X . Our main concern is to characterize L p -maximal regularity and to give an explicit approximation of the problem (P).

How to cite

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Laasri, Hafida, and El-Mennaoui, Omar. "Stability for non-autonomous linear evolution equations with $L^p$-maximal regularity." Czechoslovak Mathematical Journal 63.4 (2013): 887-908. <http://eudml.org/doc/260760>.

@article{Laasri2013,
abstract = {We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem \[ (\{\rm P\}) \{\left\lbrace \begin\{array\}\{ll\} \dot\{u\}(t)+A(t)u(t)=f(t)\quad t\text\{-a.e. on\} [0,\tau ], u(0)=0, \end\{array\}\right.\} \] where $A\colon [0,\tau ]\rightarrow \mathcal \{L\}(X,D)$ is a bounded and strongly measurable function and $X$, $D$ are Banach spaces such that $D\underset\{d\}\{\rightarrow \}\{\hookrightarrow \}X$. Our main concern is to characterize $L^p$-maximal regularity and to give an explicit approximation of the problem (P).},
author = {Laasri, Hafida, El-Mennaoui, Omar},
journal = {Czechoslovak Mathematical Journal},
keywords = {maximal regularity; on-autonomous evolution equation; stability for linear evolution equation; integrability for linear evolution equation; maximal regularity; non-autonomous evolution equation; stability; integrability},
language = {eng},
number = {4},
pages = {887-908},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability for non-autonomous linear evolution equations with $L^p$-maximal regularity},
url = {http://eudml.org/doc/260760},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Laasri, Hafida
AU - El-Mennaoui, Omar
TI - Stability for non-autonomous linear evolution equations with $L^p$-maximal regularity
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 887
EP - 908
AB - We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem \[ ({\rm P}) {\left\lbrace \begin{array}{ll} \dot{u}(t)+A(t)u(t)=f(t)\quad t\text{-a.e. on} [0,\tau ], u(0)=0, \end{array}\right.} \] where $A\colon [0,\tau ]\rightarrow \mathcal {L}(X,D)$ is a bounded and strongly measurable function and $X$, $D$ are Banach spaces such that $D\underset{d}{\rightarrow }{\hookrightarrow }X$. Our main concern is to characterize $L^p$-maximal regularity and to give an explicit approximation of the problem (P).
LA - eng
KW - maximal regularity; on-autonomous evolution equation; stability for linear evolution equation; integrability for linear evolution equation; maximal regularity; non-autonomous evolution equation; stability; integrability
UR - http://eudml.org/doc/260760
ER -

References

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