Related papers: Asymptotic Self-Similarity for Solutions of Partia…
In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow…
In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…
We discuss spherically symmetric perfect fluid solutions of Einstein's equations which have equation of state ($p=\alpha \mu$) and which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. For each…
In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped $\sigma$-evolution equations in $L^2$-sense. Depending on the parameters $\sigma$ and $\delta$ we would…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.
We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and $+\infty$.…
In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium…
The study of asymptotic properties of solutions to differential equations has a long and arduous history, with the most significant advances having been made in the development of quantum mechanics. A very powerful method of analysis is…
This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in $\mathbb{R}^d$. By a Laplace transform argument, we prove that the decay rate of the solution as…
In this paper, we investigate the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive optimal estimates, where the background metrics are not assumed…
In the present paper, we study the long time behaviour of the solutions of the second grade fluids equations in dimension 3. Using scaling variables and energy estimates in weighted Sobolev spaces, we describe the first order asymptotic…
The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy.…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
We consider wave equations with a special type of log-fractional damping. We study the Cauchy problem for this model in the whole space, and we obtain an asymptotic profile and optimal estimates of solutions as time goes to infinity in…
In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the…
We consider the spatially homogeneous Boltzmann equation for ballistic annihilation in dimension d 2. Such model describes a system of ballistic hard spheres that, at the moment of interaction, either annihilate with probability $\alpha$…
We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…