On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points
- 105 Downloads
In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.
Keywordssecond initial boundary value problem Schrödinger systems generalized solution regularity asymptotic behavior
MSC 201035B40 35B65 35G99
Unable to display preview. Download preview PDF.
- N.T. Anh, N.M. Hung: Asymptotic formulas for solutions of parameter-depending elliptic boundary-value problems in domains with conical points. Electron. J. Differ. Equ. No. 125 (2009), 1–21.Google Scholar
- N.M. Hung: The first initial boundary value problem for Schrödinger systems in non-smooth domains. Diff. Uravn. 34 (1998), 1546–1556. (In Russian.)Google Scholar
- N.M. Hung, N.T.K. Son: Existence and smoothness of solutions to second initial boundary value problems for Schrödinger systems in cylinders with non-smooth base. Electron. J. Differ. Equ., No. 35 (2008), 1–11.Google Scholar
- N.M. Hung, T.X. Tiep, N.T.K. Son: Cauchy-Neumann problem for second-order general Schrödinger equations in cylinders with non-smooth bases. Bound. Value Probl., Vol. 2009, Article ID 231802 (2009), 1–13.Google Scholar
- A. Kokotov, B.A. Plamenevskiĭ: On the asymptotics on solutions to the Neumann problem for hyperbolic systems in domains with conical points. Algebra anal. 16 (2004) (In Russian.); English transl. St. Petersburg Math. J. 16 (2005), 477–506.Google Scholar
- V.G. Kondratiev: Boundary value problems for elliptic equations in domains with conical or angular points. Tr. Mosk. Mat. O.-va 16 (1967), 209–292. (In Russian.)Google Scholar
- V.G. Kondratiev: Singularities of solutions of Dirichlet problem for second-order elliptic equations in a neighborhood of edges. Differ. Equ. 13 (1977), 2026–2032. (In Russian.)Google Scholar
- S.A. Nazarov, B.A. Plamenevskiĭ: Elliptic Problems in Domains with Piecewise-Smooth Boundary. Nauka, Moskva, 1990. (In Russian.)Google Scholar