Generalized maximum principles for linear elliptic equations
Generalized n-dimensional Gronwall's inequality and its applications to non-selfadjoint and non-linear hyperbolic equations
Generalized periodic solutions of nonlinear telegraph equations (Preliminary communication)
Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices.
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.
Generalized Solutions to Semilinear Hyperbolic Systems.
Générateurs infinitésimaux et propriétés géométriques pour certaines équations complètement non linéaires.
Nous nous proposons, dans ce travail, d'étudier certaines propriétés géométriques telles que diverses symétries et diverses concavités radiales, directionnelles, etc., pour des équations completement non linéaires (...).
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of -Laplacian type. If and the right-hand side is a Radon measure with singularity of order at , then any supersolution in has singularity of order at least at . In the proof we exploit a pointwise estimate of -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.
Generation of analytic semigroups by elliptic operators of second order in Hölder spaces
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.
Generic behaviour of one-dimensional blow up patterns
Generic properties of nonlinear boundary value problems
Generic properties of von Kármán equations
Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator.
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...
Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations.
Geometrische Eigenschaften der Lösungen der Differentialgleichung (1-zz)2wzz - n(n + 1) w= 0.