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.
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Geometry of the rolling ellipsoid
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....
Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators
The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in , without any restriction on the characteristic polyhedron.
Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
Global and blowup solutions of quasilinear parabolic equation with critical Sobolev equation and lower energy initial value.
Global and exponential attractors for a Caginalp type phase-field problem
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system
The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution to this problem. Moreover, a necessary and sufficient condition for the non-global existence...
Global asymptotic stability of 3-species mutualism models with diffusion and delay effects.
Global Asymptotic Stability of Equilibria in Models for Virus Dynamics
In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this...
Global asymptotic stability of solutions to nonlinear marine riser equation.
Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
Global attraction to solitary waves in models based on the Klein-Gordon equation.
Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models
In this paper, we discuss the special diffusive hematopoiesis model with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.
Global attractor and finite dimensionally for a class of dissipative equations of BBM's type.
Global Attractor for a Class of Parabolic Equations with Infinite Delay
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.