scholarly journals Uniform decay rates for the energy of weakly damped defocusing semilinear Schrödinger equations with inhomogeneous Dirichlet boundary control

2011 ◽  
Vol 251 (7) ◽  
pp. 1841-1863 ◽  
Author(s):  
Türker Özsarı ◽  
Varga K. Kalantarov ◽  
Irena Lasiecka
Keyword(s):  
Boundary Control ◽  
Dirichlet Boundary ◽  
Decay Rates ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dirichlet Boundary Control ◽  
Uniform Decay

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

Energy corrected FEM for optimal Dirichlet boundary control problems

2018 ◽  
Vol 139 (4) ◽  
pp. 913-938 ◽  
Author(s):  
Lorenz John ◽  
Piotr Swierczynski ◽  
Barbara Wohlmuth
Keyword(s):  
Boundary Control ◽  
Dirichlet Boundary ◽  
Control Problems ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problems
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