On a class of nonhomogeneous quasilinear problem involving Sobolev spaces with variable exponent.
On a generalized nonlinear equation of Schrödinger type.
On a nonlocal problem for a confined plasma in a Tokamak
The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms and , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.
On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type.
On Bardina and Approximate Deconvolution Models
We first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution”...
On generalized solutions to the wave equation in canonical form [Book]
On global solutions to a nonlinear Alfvén wave equation
We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.
On initial boundary value problems with equivalued surface for nonlinear parabolic equations.
On optimal decay rates for weak solutions to the Navier-Stokes equations in
This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in . Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound
On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities
We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.
On spaces and
On the blow-up set for non-Newtonian equation with a nonlinear boundary condition.
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition∫ 1 ∞ P ( t ) t 2 d t = ∞ .
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition
On the Convergence of Finite Difference Scheme for Elliptic Equation With Coefficients Containing Dirac Distribution
On the convolution equations over the quarter-plane.
On the existence and regularity of solutions of linear equations in spaces
On the global attractors for a class of semilinear degenerate parabolic equations
We prove the existence and upper semicontinuity with respect to the nonlinearity and the diffusion coefficient of global attractors for a class of semilinear degenerate parabolic equations in an arbitrary domain.
On the global existence for a regularized model of viscoelastic non-Newtonian fluid
We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like (p > 6/5), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...