Analyticity and near optimal time boundary controllability for the linear Klein-Gordon equation

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• 作者：R.S.O. Nunes^a ; ^{ruiksonsillas@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; W.D. Bastos^b ; ¹ ; ^{waldemar@ibilce.unesp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Klein&ndash ; Gordon equation ; Time analyticity ; Optimal time boundary controllability ; Exact controllability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：394-406
• 全文大小：353 K

文摘

We study time analyticity for the solutions of the linear Klein–Gordon equation in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303997&_mathId=si1.gif&_user=111111111&_pii=S0022247X16303997&_rdoc=1&_issn=0022247X&md5=b4e198cff0efb14d47dfcc852cbc4ae7" title="Click to view the MathML source">R^Nclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^N$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303997&_mathId=si2.gif&_user=111111111&_pii=S0022247X16303997&_rdoc=1&_issn=0022247X&md5=4b96c4f8026f39b93a2c398a5158b181" title="Click to view the MathML source">N≥1class="mathContainer hidden">class="mathCode">$N\ge 1$ and use it to obtain essentially optimal time boundary controllability in piecewise smooth domains. The initial state has finite energy and the control is square integrable.