ncku-talk2010-07-13

NCTS(South) Topical Program in Applied Math-Partial Differential Equations

DATE 2010-07-13　14:10-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. Tai-Peng Tsai (蔡岱朋教授)（Dept. of Math., The University of British Columbia, Canada）

TITLE Small solutions of nonlinear Schrödinger equations near first excited states (I)~(II)

ABSTRACT Consider a nonlinear Schrödinger equation in $R^3$ whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in $H^1 cap L^1(R^3)$ and inside a neighborhood of the first excited state family are shown to converge to either a first excited state or a ground state at time infinity. An essential part of our analysis is on the linear and nonlinear estimates near nonlinear excited states, around which the linearized operators have eigenvalues with nonzero real parts and their corresponding eigenfunctions are not uniformly localized in space.
This is a joint work with Kenji Nakanishi and Tuoc Van Phan. In the minicourse, lecture 1 considers the one eigenvalue case, lecture 2 the two eigenvalue case, lectures 3 and 4 the many eigenvalue case including the above mentioned result.

NCTS(South) Topical Program in Applied Math-Partial Differential Equations

DATE	2010-07-13　14:10-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. Tai-Peng Tsai (蔡岱朋教授)（Dept. of Math., The University of British Columbia, Canada）

TITLE	Small solutions of nonlinear Schrödinger equations near first excited states (I)~(II)

ABSTRACT	Consider a nonlinear Schrödinger equation in $R^3$ whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in $H^1 cap L^1(R^3)$ and inside a neighborhood of the first excited state family are shown to converge to either a first excited state or a ground state at time infinity. An essential part of our analysis is on the linear and nonlinear estimates near nonlinear excited states, around which the linearized operators have eigenvalues with nonzero real parts and their corresponding eigenfunctions are not uniformly localized in space. This is a joint work with Kenji Nakanishi and Tuoc Van Phan. In the minicourse, lecture 1 considers the one eigenvalue case, lecture 2 the two eigenvalue case, lectures 3 and 4 the many eigenvalue case including the above mentioned result.