In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilin...In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.展开更多
The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy...The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H^1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.展开更多
基金Project supported by the Fundacao para a Ciencia e Tecnologia, Financiamento Base (Nos. 2008-ISFL-1-209,2008-ISFL-1-297)the Fundacao para a Ciencia e Tecnologia Grant (No. PTDC/MAT/110613/2009)
文摘In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.
基金supported by the Fundacao para a Ciência e Tecnologia(Portugal)(Nos.PEstOE/MAT/UI0209/2013,UID/MAT/04561/2013,PTDC/FIS-OPT/1918/2012,UID/FIS/00618/2013)
文摘The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H^1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.
