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18 papers · 2 filters
Existence and non-existence for the collision-induced breakage equation
Ankik Kumar Giri, Philippe Laurençot
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large…
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions
Guillaume Bertoli, Christophe Besse, Gilles Vilmart
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation…
Stability of the multi-solitons of the modified Korteweg-de Vries equation
Stefan Le Coz, Zhong Wang
We establish the nonlinear stability of -soliton solutions of the modified Korteweg-de Vries (mKdV) equation. The -soliton solutions are global solutions of mKdV behaving at…
Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation
Antonio J. Fernández, Louis Jeanjean, Rainer Mandel +1
We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the norm (the \textit{mass}) } is kept fixe…
Invasion into remnant instability: a case study of front dynamics
Gregory Faye, Matt Holzer, Arnd Scheel +1
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant insta…
Separation of domain walls with nonlocal interaction and their renormalised energy by -convergence in thin ferromagnetic films
Radu Ignat, Roger Moser
We analyse two variants of a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter . The model gives rise to trans…