Forced periodic oscillations in the climate system via an energy balance model
Forced periodic vibrations of an elastic system with elastico-plastic damping
We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations for an arbitrary (sufficiently smooth) periodic right-hand side , where denotes the Laplace operator with respect to , and is the Ishlinskii hysteresis operator. For this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.
Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem
Forced vibrations of wave equations with non-monotone nonlinearities
Free vibrations for the equation of a rectangular thin plate
In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.
Galerkin approximations for nonlinear evolution inclusions
In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.
Generalized periodic solutions of nonlinear telegraph equations (Preliminary communication)
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.
Global sovability for the degenerate Krichhoff equation with real anlytic data.
Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix . Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with -Sobolev norm growing in time. We establish the existence of solutions with polynomial time estimates. More exactly, there is such that for any we find a solution and a time such that . Moreover, the time satisfies the polynomial bound .
Hard implicit function theorem and small periodic solutions to partial differential equations
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Hopf bifurcation with the spatial average of an activator in a radially symmetric free boundary problem.
Hysteresis and Periodic Solutions of Semilinear and Quasilinear Wave Equations.
Indices of Orlicz spaces and some applications
We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.
Infinitely many periodic solutions for variable exponent systems.
Infinitely many periodic solutions of nonlinear wave equations on .
Invariant measures for Burgers equation with stochastic forcing.
Invariant regions associated with quasilinear damped wave equations
Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems.