Instability of standing waves for the generalized Davey-Stewartson system
Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field
Instability of the stationary solutions of generalized dissipative Boussinesq equation
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.
Instability of traveling waves for a generalized diffusion model in population problems.
Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities
We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...
Instantaneous blow-up of solutions to a class of hyperbolic inequalities.
Instantaneous shrinking of the support for solutions to certain parabolic equations and systems
The paper contains conditions ensuring instantaneous shrinking of the support for solutions to semilinear parabolic equations with compactly supported coefficients of nonlinear terms and reaction-diffusion systems.
Intégrabilité d'une classe de systèmes de lois de conservation.
Integrability for solutions to quasilinear elliptic systems
In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.
Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation.
Integral inequalities and summability of solutions of some differential problems
The aim of this note is to indicate how inequalities concerning the integral of on the subsets where |u(x)| is greater than k () can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of on the subsets where |u(x)| is less than k () or...
Interaction contrôlée dans les équations aux dérivées partielles non linéaires
Interaction des singularités pour les équations aux dérivées partielles non linéaires
Interaction d'ondes simples pour des équations complètement non-linéaires
Interaction of progressing waves through a nonlinear potential
Interaction of Turing and Hopf Modes in the Superdiffusive Brusselator Model Near a Codimension Two Bifurcation Point
Spatiotemporal patterns near a codimension-2 Turing-Hopf point of the one-dimensional superdiffusive Brusselator model are analyzed. The superdiffusive Brusselator model differs from its regular counterpart in that the Laplacian operator of the regular model is replaced by ∂α/∂|ξ|α, 1 < α < 2, an integro-differential operator that reflects the nonlocal behavior of superdiffusion. The order of the operator, α, is a measure of the rate of ...
Interface and mixed boundary value problems on -dimensional polyhedral domains.
Interface dynamics for an anisotropic Allen-Cahn equation
Interior gradient estimates for nonuniformly parabolic equations. II.
Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets