Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain.
Global existence of smooth solutions for the compressible viscous fluid flow with radiation in
This paper is concerned with the 3-D Cauchy problem for the compressible viscous fluid flow taking into account the radiation effect. For more general gases including ideal polytropic gas, we prove that there exists a unique smooth solutions in , provided that the initial perturbations are small. Moreover, the time decay rates of the global solutions are obtained for higher-order spatial derivatives of density, velocity, temperature, and the radiative heat flux.
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 well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay
We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism...
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...