Maximal regularity for second order non-autonomous Cauchy problems

Charles J. K. Batty, Ralph Chill, and Sachi Srivastava. "Maximal regularity for second order non-autonomous Cauchy problems." Studia Mathematica 189.3 (2008): 205-223. <http://eudml.org/doc/284745>.

@article{CharlesJ2008,
abstract = {We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has $L^\{p\}$-maximal regularity. Then we establish $L^\{p\}$-maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).},
author = {Charles J. K. Batty, Ralph Chill, Sachi Srivastava},
journal = {Studia Mathematica},
keywords = {maximal regularity; non-autonomous; second order Cauchy problem},
language = {eng},
number = {3},
pages = {205-223},
title = {Maximal regularity for second order non-autonomous Cauchy problems},
url = {http://eudml.org/doc/284745},
volume = {189},
year = {2008},
}

TY - JOUR
AU - Charles J. K. Batty
AU - Ralph Chill
AU - Sachi Srivastava
TI - Maximal regularity for second order non-autonomous Cauchy problems
JO - Studia Mathematica
PY - 2008
VL - 189
IS - 3
SP - 205
EP - 223
AB - We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has $L^{p}$-maximal regularity. Then we establish $L^{p}$-maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).
LA - eng
KW - maximal regularity; non-autonomous; second order Cauchy problem
UR - http://eudml.org/doc/284745
ER -