Time fluctuations in a population model of adaptive dynamics

Under concavity assumptions on the reaction term, we prove that the solution converges to a Dirac mass whose evolution in time is driven by a Hamilton–Jacobi equation with

The stated result follows by approximation since solutions of the porous medium equation depend continuously on the initial data.. Using these estimates and arguing as

McCoy [17, Section 6] also showed that with sufficiently strong curvature ratio bounds on the initial hypersur- face, the convergence result can be established for α > 1 for a

We show that the entropy method can be used to prove exponential con- vergence towards equilibrium with explicit constants when one considers a reaction-diffusion system

L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » ( http://rendiconti.math.unipd.it/ ) implique l’accord avec les

In other words, transport occurs with finite speed: that makes a great difference with the instantaneous positivity of solution (related of a “infinite speed” of propagation

The proofs of Theorems 2.2 and 2.5 are based on the representations of the density and its derivative obtained by using Malliavin calculus and on the study of the asymptotic behavior

In this section, we study the large behaviour of non-negative solutions to the Hamilton-Jacobi equation (4.6) with initial data in C 0 ( R N ) and show their convergence to a