5 papers
Damped nonlinear Ginzburg-Landau equation with saturation. Part II. Strong Stabilization
Pascal Bégout, Jesús Ildefonso DÃaz
We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between th…
Damped nonlinear Ginzburg-Landau equation with saturation. Part I. Existence of solutions on general domains
Pascal Bégout, Jesús Ildefonso DÃaz
We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between th…
Strong stabilization of damped nonlinear Schr{ö}dinger equation with saturation on unbounded domains
Pascal Bégout, Jesús Ildefonso DÃaz
We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term …
Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term
Jesús Ildefonso DÃaz
In the so-called Child-Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area , separated t…
On the compactness of the support of solitary waves of the complex saturated nonlinear Schr{ö}dinger equation and related problems
Pascal Bégout, Jesús Ildefonso DÃaz
We study the vectorial stationary Schr{ö}dinger equation -u + a U + b u = F, with a saturated nonlinearity U = u/|u| and with some complex coefficients (a, b) C 2 . Besi…