Generalized Functions Solutions of Monotone and Semilinear Parabolic Equations.
Generalized solutions to hybrid dynamical systems
Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.
Geometric optics and instability for NLS and Davey-Stewartson models
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with Gauge invariant power-law nonlinearities and nonlocal perturbations. The model includes the Davey-Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variants. Our analysis reveals a new localization phenomenon for nonlocal perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative order Sobolev...
Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems
We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the source terms...
Global asymptotic stability of 3-species mutualism models with diffusion and delay effects.
Global asymptotic stability of solutions to nonlinear marine riser equation.
Global attractors for two-phase Stefan problems in one-dimensional space.
Global behavior for a diffusive predator-prey model with stage structure and nonlinear density restriction. I: The case in .
Global behavior for a diffusive predator-prey model with stage structure and nonlinear density restriction. II: The case in .
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.
Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
Global existence and nonlinear boundary stabilization of an elastic system. (Existence globale et stabilisation frontière non linéaire d'un système d'élasticité.)
Global existence and stability of some semilinear problems
We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.
Global existence of solutions of parabolic problems with nonlinear boundary conditions
Global in time solutions to quasilinear telegraph equations involving operators with time delay
The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.
Global in Time Stability of Steady Shocks in Nozzles
We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global regularity for the 3D MHD system with damping
We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.
Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.