32 citations · 65 across the 17 of their papers we have counts for
15 papers · 1 filter
Generic transversality of travelling fronts, standing fronts, and standing pulses for parabolic gradient systems
Romain Joly, Emmanuel Risler
For nonlinear parabolic systems of the form \[ \partial_t w(x,t) = \partial_{x}^2 w(x,t) - \nabla V\bigl(w(x,t)\bigr) \,, \] the following conclusions are proved to hold genericall…
Control of the Schrödinger equation by slow deformations of the domain
Alessandro Duca, Romain Joly, Dmitry Turaev
The aim of this work is to study the controllability of the Schrödinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-Δu(t)~~~~~\text{ on }Ω(t) \tag{} \end{e…
Schrödinger equation in moving domains
Alessandro Duca, Romain Joly
We consider the Schr\''odinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-Δu(t)~~~~~\text{ on }Ω(t) \tag{} \end{equation}where is…
Asymptotic self-similarity in diffusion equations with nonconstant radial limits at infinity
Thierry Gallay, Romain Joly, Geneviève Raugel
We study the long-time behavior of localized solutions to linear or semilinear parabolic equations in the whole space , where , assuming that the diffusion m…
Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations
Pavol Brunovský, Romain Joly, Geneviève Raugel
In this paper, we consider the scalar reaction-diffusion equations on a bounded domain of class . We show that the h…
Decay of semilinear damped wave equations:cases without geometric control condition
Romain Joly, Camille Laurent
We consider the semilinear damped wave equation . In this article, we obtain the first results concerning…