start-ver=1.4
cd-journal=joma
no-vol=89
cd-vols=
no-issue=1
article-no=
start-page=123
end-page=160
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2004
dt-pub=20047
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Abstract cauchy problems for quasi-linear evolution equations in the sense of hadamard
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=<p>thispaper is devoted to the well-posedness of abstract cauchy problems for quasi-linear evolution equations. the notion of hadamard well-posedness is considered, and a new type of stability condition is introduced from the viewpoint of the theory of finite difference approximations. the result obtained here generalizes not only some results on abstract cauchy problems closely related with the theory of integrated semigroups or regularized semigroups but also the kato theorem on quasi-linear evolution equations. an application to some quasi-linear partial differential equation of weakly hyperbolic type is also given.</p>

en-copyright=
kn-copyright=

en-aut-name=TanakaNaoki
en-aut-sei=Tanaka
en-aut-mei=Naoki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=
kn-affil=Okayama University
en-keyword=abstract cauchy problem in the sense of hadamard
kn-keyword=abstract cauchy problem in the sense of hadamard
en-keyword=regularized semigroup
kn-keyword=regularized semigroup
en-keyword=abstract quasi-linear evolution equation
kn-keyword=abstract quasi-linear evolution equation
en-keyword=stability condition
kn-keyword=stability condition
en-keyword=  finite difference approximation.
kn-keyword=  finite difference approximation.
END