Conditional stability for a Cauchy problem for the ultrahyperbolic Schrodinger equation
Ismet Golgeleyen, Ozlem Kaytmaz
article (Uluslararası, Hakemli) | Yazar(lar): Ismet Golgeleyen, Ozlem Kaytmaz | Yıl: 2022 | Dergi/Kurum: APPLICABLE ANALYSIS | İndeks: WOS.SCI | DOI: 10.1080/00036811.2020.1781829 | Anahtar Kelimeler: Ultrahyperbolic Schrodinger equation, Cauchy problem, conditional stability, Carleman inequality — Özet: In this work,
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.