Related papers: A non-autonomous bifurcation problem for a non-loc…
We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than…
In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover…
The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing…
We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb R\times \mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…
This work investigates the long-time asymptotic behavior of a diffusing passive scalar advected by fluid flow in a straight channel with a periodically varying cross-section. The goal is to derive an asymptotic expansion for the scalar…
We consider a general hyperbolic model of chemotaxis in the multidimensional case. For this system we show the global existence of smooth solutions to the Cauchy problem and we determine their asymptotic behavior. Since this model does not…
We study the asymptotic behavior of blow-up solutions of the heat equation with nonlinear boundary conditions. In particular, we classify the asymptotic behavior of blow-up solutions and investigate the spacial singularity of their blow-up…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
In this paper, the method of constructing the asymptotics of the fundamental solution of the Cauchy problem for a degenerate linear parabolic equation with small diffusion is considered. Based on the results obtained in \cite{dn}, the study…
The Cauchy problem for a quasi-linear parabolic equation with a small parameter at a higher derivative is considered. The initial step-like function contains another small parameter. Formal asymptotic solutions of the problem in small…
We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and…
In this paper we study the asymptotic behavior of nonoscillatory solutions for high order differential equations of Poincar\'e type. We introduce two new and more weak than classical hypotheses on the coefficients, which implies a well…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…
We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP) equation with a nonlocal diffusion and an almost-periodic nonlinearity. By employing and adapting the theory of homogenization, we show that solutions of this equation…
The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem…
We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…
In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in…