Interaction contrôlée dans les équations aux dérivées partielles non linéaires
Interaction de chocs
Interaction des singularités pour 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 d'ondes simples pour des équations complètement non-linéaires
Interaction of progressing waves through a nonlinear potential
Interactions totalement non linéaires
Interactions trilinéaires résonantes
Interface model coupling via prescribed local flux balance
This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary...
Interface tracking method for compressible multifluids
This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell...
Interior feedback stabilization of wave equations with time dependent delay.
Interior point control and observation for the wave equation.
Intermittency properties in a hyperbolic Anderson problem
We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison,...
Internal modes of solitons and near-integrable highly-dispersive nonlinear systems.
Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation.
Invariant regions associated with quasilinear damped wave equations
Invariant sets and connecting orbits for nonlinear evolution equations at resonance
We study the problem of existence of orbits connecting stationary points for the nonlinear heat and strongly damped wave equations being at resonance at infinity. The main difficulty lies in the fact that the problems may have no solutions for general nonlinearity. To address this question we introduce geometrical assumptions for the nonlinear term and use them to prove index formulas expressing the Conley index of associated semiflows. We also prove that the geometrical assumptions are generalizations...
Invariant tensors and partial differential equations.
Invariants, conservation laws and time decay for a nonlinear system of Klein-Gordon equations with Hamiltonian structure
We discuss invariants and conservation laws for a nonlinear system of Klein-Gordon equations with Hamiltonian structure ⎧, ⎨ ⎩ for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). Based on Morawetz-type identity, we prove that solutions to the above system decay to zero in local L²-norm, and local energy also decays to zero if the initial energy satisfies , and F₁(|u|²,|v|²)|u|² + F₂(|u|²,|v|²)|v|² - F(|u|²,|v|²) ≥ aF(|u|²,|v|²) ≥ 0, a > 0.