Unicité du problème de Cauchy pour une classe d'opérateurs différentiels à caractéristiques de multiplicité constante
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation . The approach is based on suitable iterative fixed point methods in based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.
We consider the first initial boundary value problem for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The results, in particular, improve some recent ones for nonautonomous p-Laplacian equations.
Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such thatwhere (resp. ) are the Green functions of (resp. ) on .
We consider complex-valued solutions of the Ginzburg–Landau equation on a smooth bounded simply connected domain of , , where is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of , as , is to establish uniform bounds for the gradient, for some . We review some recent techniques developed in...
We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of , N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...
We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.
We review some recent results in quantitative stochastic homogenization for divergence-form, quasilinear elliptic equations. In particular, we are interested in obtaining -type bounds on the gradient of solutions and thus giving a demonstration of the principle that solutions of equations with random coefficients have much better regularity (with overwhelming probability) than a general equation with non-constant coefficients.
It is well known that people can derive the radiation MHD model from an MHD- approximate model. As pointed out by F. Xie and C. Klingenberg (2018), the uniform regularity estimates play an important role in the convergence from an MHD- approximate model to the radiation MHD model. The aim of this paper is to prove the uniform regularity of strong solutions to an isentropic compressible MHD- approximate model arising in radiation hydrodynamics. Here we use the bilinear commutator and product estimates...