Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions.
Global existence of solutions of parabolic problems with nonlinear boundary conditions
Global existence of solutions to Navier-Stokes equations in cylindrical domains
We prove the existence of global and regular solutions to the Navier-Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the x₃-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval [0,T], where T > 0 is large, on the assumption that the L₂-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the direction of...
Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials
This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature , an evolution equation for the phase change parameter , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable . The main novelty of the model...
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 exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure
We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a -pseudo almost automorphic solution. The...
Global Hölder estimates for equations of Monge-Ampère type.
Global in time solutions to quasilinear telegraph equations involving operators with time delay
The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.
Global in Time Stability of Steady Shocks in Nozzles
We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Global bounds for a class of quasilinear parabolic equations.
Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that...
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global optimal regularity for the parabolic polyharmonic equations.
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 Regular Solutions for the Dynamic Antiplane Shear Problem in Nonlinear Viscoelasticity.
Global regularity for solutions of the minimal surface equation with continuous boundary values
Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity and with natural growth
In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for...
Global regularity for the 3D MHD system with damping
We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.