Asymptotic integration of parabolic problems with large high-frequency summands.
Asymptotic observables and Coulomb scattering for the Dirac equation
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.
Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation.
Asymptotic profile of solutions for the critical Sobolev type equation on a half-line.
Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion.
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
We study the leading order behaviour of positive solutions of the equation , where , and when is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of , and . The behavior of solutions depends sensitively on whether is less, equal or bigger than the critical Sobolev exponent . For the solution asymptotically coincides with the solution of the equation in which the last term is absent. For the solution asymptotically coincides...
Asymptotic properties of steady plane solutions of the Navier-Stokes equations with bounded Dirichlet integral
Asymptotic properties of the magnetic integrated density of states.
Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary.
Asymptotic representations for solutions of bisingular problems.
Asymptotic self-similar blow-up for a model of aggregation
In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between diffusion...
Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space
Asymptotic solutions of diffusion models for risk reserves.
Asymptotic solutions to Fuchsian equations in several variables
The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.
Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows
Asymptotic stability for a nonlinear evolution equation
We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation .
Asymptotic stability of a linear Boltzmann-type equation
We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.
Asymptotic stability of linear conservative systems when coupled with diffusive systems
In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not have the asymptotic...
Asymptotic stability of linear conservative systems when coupled with diffusive systems
In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not have the asymptotic property. ...