Flow invariance for semilinear evolution equations under generalized dissipativity conditions
- 作者：Paul Georgescu ; Gheorghe Moroş ; anu
- 关键词：Semilinear evolution equations ; Flow invariance ; Generalized dissipativity ; Discrete schemes ; Subtangential condition ; Stability condition
- 刊名：Nonlinear Analysis
- 出版年：2008
- 期刊代码：43_0362546x
- 类别：mt
- 出版时间：15 January 2008
- 卷：68
- 期：2
- 页码：443-455
- 文件大小：293 K
摘要
Let l1">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml1&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=e467bd3f87d476d96ab448ee183b3b10" title="Click to view the MathML source">X be a real Banach space, let l2">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml2&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=2819db69d98884537506f5b5172e6f52" title="Click to view the MathML source">A:D(A)
lt="subset of" border=0>X→X be a linear operator which is the infinitesimal generator of a l3">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml3&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=933d44dddb7e9dde55be66982e86e2e4" title="Click to view the MathML source">(C0)-semigroup and let l4">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml4&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=6a13a215f2cd07ae8c7219547c9e33dd" title="Click to view the MathML source">B:Dlt="subset of" border=0>X→X be a nonlinear perturbation which is continuous on level sets of l5">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml5&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=77a191a3af410f0bbc802a573cecf192" title="Click to view the MathML source">D with respect to a lower semicontinuous (l.s.c.) functional l6">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml6&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=5a205f8707b69ab35ab1d7142ce533be" title="Click to view the MathML source">φ. We discuss the existence of a nonlinear semigroup l7">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml7&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=4aacd8c5a1cef2c4de85333f62da6b5e" title="Click to view the MathML source">S providing mild solutions to the semilinear abstract Cauchy problem
lt="subset of" border=0>X→X be a linear operator which is the infinitesimal generator of a l3">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml3&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=933d44dddb7e9dde55be66982e86e2e4" title="Click to view the MathML source">(C0)-semigroup and let l4">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml4&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=6a13a215f2cd07ae8c7219547c9e33dd" title="Click to view the MathML source">B:Dlt="subset of" border=0>X→X be a nonlinear perturbation which is continuous on level sets of l5">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml5&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=77a191a3af410f0bbc802a573cecf192" title="Click to view the MathML source">D with respect to a lower semicontinuous (l.s.c.) functional l6">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml6&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=5a205f8707b69ab35ab1d7142ce533be" title="Click to view the MathML source">φ. We discuss the existence of a nonlinear semigroup l7">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml7&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=4aacd8c5a1cef2c4de85333f62da6b5e" title="Click to view the MathML source">S providing mild solutions to the semilinear abstract Cauchy problem lass="art">
lign="center"> lign="center" width="95%">l8">l8&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=4767e9bddf3ae26349786d1fd1c329e6"> lt="Click to view the MathML source" align="absbottom" border="0" height=15 width=312>
lass="art"> and satisfying a certain Lipschitz-like estimation and an exponential growth condition. Using the discrete schemes approximation, it is proved that the combination of a subtangential condition and a semilinear stability condition in terms of a metric-like functional is necessary and sufficient for the generation of such a semigroup l9">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4MKV2JG-2&_mathId=mml9&_user=10&_cdi=5659&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=5cf691a561843c75c7e05820982720f6" title="Click to view the MathML source">S.