Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain.
Global existence, uniqueness, and asymptotic behavior of solution for -Laplacian type wave equation.
Global existence versus blow up for some models of interacting particles
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
Global pointwise a priori bounds and large time behaviour for a nonlinear system describing the spread of infectious disease
This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.
Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.
Global solutions and finite time blow up for damped semilinear wave equations
Global solutions and quenching to a class of quasilinear parabolic equations.
Global solutions for a nonlinear hyperbolic equation with boundary memory source term.
Global solutions for a nonlinear wave equation with the -Laplacian operator.
Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations.
Global stability of travelling fronts for a damped wave equation with bistable nonlinearity
We consider the damped wave equation on the whole real line, where is a bistable potential. This equation has travelling front solutions of the form which describe a moving interface between two different steady states of the system, one of which being the global minimum of . We show that, if the initial data are sufficiently close to the profile of a front for large , the solution of the damped wave equation converges uniformly on to a travelling front as . The proof of this global stability...
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.
Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
Global weak solutions of the wave map system to compact homogeneous spaces.
Global φ-attractor for a modified 3D Bénard system on channel-like domains
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
Grandient Estimates for Degenerate Diffusion Equations. I.
Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients
We study the first eigenpair of a Dirichlet spectral problem for singularly perturbed convection-diffusion operators with oscillating locally periodic coefficients. It follows from the results of [A. Piatnitski and V. Rybalko, On the first eigenpair of singularly perturbed operators with oscillating coefficients. Preprint www.arxiv.org, arXiv:1206.3754] that the first eigenvalue remains bounded only if the integral curves of the so-called effective drift have a nonempty ω-limit set. Here we consider...
Growing Sobolev norms for the cubic defocusing Schrödinger equation
This text aims to describe results of the authors on the long time behavior of NLS on product spaces with a particular emphasis on the existence of solutions with growing higher Sobolev norms.
Growth and accretion of mass in an astrophysical model
We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.
Growth and accretion of mass in an astrophysical model, II
Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.