Abstract
In this work, we first establish a local Carleman estimate for the ultrahyperbolic Schrodinger equation which arises in some theories of modern physics such as quantum mechanics and string theory. Next, we prove a Holder stability estimate for the Cauchy Problem. In the proof, we introduce a suitable cut-off function and extend Cauchy data in a Sobolev space to reduce the problem to another problem for functions with compact supports and then we apply the Carleman estimate.
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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.SCI
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Language
English
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Article Type
None
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Keywords
Ultrahyperbolic Schrodinger equation Cauchy problem conditional stability Carleman inequality