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A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...

Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem, Henda El Fekih, Hejer Metoui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Singular perturbations in foliations.

Giko Ikegami (1989)

Inventiones mathematicae

Singular solutions for the differential equation with $p$ -Laplacian

Miroslav Bartušek (2005)

Archivum Mathematicum

In the paper a sufficient condition for all solutions of the differential equation with $p$ -Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations $(| y^{'} |^{p - 1} y^{'})^{'} + r (t) {| y |}^{λ} sgn y = 0$ , $r > 0$ are given for which singular solutions exist (for any $p > 0$ , $λ > 0$ , $p \neq λ$ ).

Singular solutions of a singular differential equation.

Kusano, Takaŝi, Naito, Manabu (2000)

Journal of Inequalities and Applications [electronic only]

Singularité analytique et perturbation singulière en dimension 2

Guy Wallet (1994)

Bulletin de la Société Mathématique de France

Singularities of vector fields

Floris Takens (1974)

Publications Mathématiques de l'IHÉS

Slow and fast systems with Hamiltonian reduced problems.

Benbachir, Maamar, Yadi, Karim, Bebbouchi, Rachid (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Smoothness property for bifurcation diagrams.

Robert Roussarie (1997)

Publicacions Matemàtiques

Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line...

Solutions approaching polynomials at infinity to nonlinear ordinary differential equations.

Philos, Christos G., Tsamatos, Panagiotis Ch. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Solutions d'une equation differentielle au deuxieme membre factorise dans les voisinages des fonctions donnees et leur stabilite

G. Pavlović (1980)

Matematički Vesnik

Solutions to Lyapunov stability problems: Nonlinear systems with continuous motions.

Grujić, Ljubomir T. (1994)

International Journal of Mathematics and Mathematical Sciences

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