On a class of nonhomogeneous quasilinear problem involving Sobolev spaces with variable exponent.
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 initial boundary value problems with equivalued surface for nonlinear parabolic equations.
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 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 local Cauchy problem for first order partial differential functional equations
A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can be obtained...
On the Neumann problem with L¹ data
We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
On the regularity for solutions of the micropolar fluid equations
On the singular behavior of solutions of a transmission problem in a dihedral.
On the solvability of Dirichlet problem for the weighted p-Laplacian
In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space .
On the solvability of superlinear and nonhomogeneous quasilinear equations.
On the solvability of the equation div in and in
We show that the equation div has, in general, no Lipschitz (respectively ) solution if is (respectively ).