On Maximal Functions and Parabolic Limits.
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 perturbed wave equations with time-dependent coefficients
On Positive L? Solutions of a Class of Elliptic Systems.
On «power-logarithmic» solutions of the Dirichlet problem for elliptic systems in , where is a d-dimensional cone
A description of all «power-logarithmic» solutions to the homogeneous Dirichlet problem for strongly elliptic systems in a -dimensional cone is given, where is an arbitrary open cone in and .
On quasiparabolical differential equations of higher order
On questions of decay and existence for the viscous Camassa–Holm equations
On radial limit functions for entire solutions of second order elliptic equations in R2.
Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for whichlimr→∞ u(reiφ) =: U(eiφ)exists for all φ ∈ [0; 2π) as a finite limit in C. We characterize the possible "radial limit functions" U. This is an analog of the work of A. Roth for entire holomorphic functions. The results seems new even for harmonic functions.
On radially symmetric solutions of some chemotaxis system
This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.
On rates of propagation for Burgers’ equation
We give asymptotic formulae for the propagation of an initial disturbance of the Burgers’ equation.
On self-similarity and stationary problem for fragmentation and coagulation models
On solutions of a perturbed fast diffusion equation
The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.
On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.
On some Klein-Gordon-Schrödinger type systems
On some properties of solutions of quasilinear degenerate parabolic equations in
We study the asymptotic behaviour near infinity of the weak solutions of the Cauchy-problem.
On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation.
On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on , is performed by taking care of possible...
On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form.
We consider the linear convection-diffusion equation associated to higher order elliptic operators⎧ ut + Ltu = a∇u on Rnx(0,∞)⎩ u(0) = u0 ∈ L1(Rn),where a is a constant vector in Rn, m ∈ N*, n ≥ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 ≤ p ≤ ∞), of the derivatives Dγu(t) of the solution of the convection-diffusion equation...