Related papers: Asymptotic behavior of Eigen's quasispecies model
We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold,…
We study numerically the semiclassical limit for the nonlinear Schroedinger equation thanks to a modification of the Madelung transform due to E.Grenier. This approach is naturally asymptotic preserving, and allows for the presence of…
We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control both on drift and diffusion coefficients. We prove that, as…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified…
Using properties of asymptotically almost periodic solutions we prove existence theorem for piece-wise continuous almost periodic solutions of differential equations with delay and impulses. We apply these results to study almost periodic…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the…
We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…
We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…
We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…
We study the asymptotic behavior of geodesics near the boundary of a conformally compact Riemannian manifold $(X,g)$. In the case where the sectional curvature at infinity is constant (the asymptotically hyperbolic case) it is known that…
We study the long-time behavior of solutions of the $k$-Hessian evolution equation $u_t=S_{k}(D^2 u)$, posed on a bounded domain of the $n$-dimensional space with homogeneous boundary conditions. To this end, we construct a separable…
We consider the problem of quasinormal modes (QNM) for strongly hyperbolic systems on stationary, asymptotically anti-de Sitter black holes, with very general boundary conditions at infinity. We argue that for a time slicing regular at the…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
Using the precise Leaver method and time-domain integration, we analyze the quasinormal modes and late-time behavior of massive neutral and charged scalar fields in the background of a charged, asymptotically flat black hole in the presence…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…
In a Hilbert space $\mathcal H$, we study the asymptotic behaviour, as time variable $t$ goes to $+\infty$, of nonautonomous gradient-like dynamical systems involving inertia and multiscale features. Given $\mathcal H$ a general Hilbert…