Asymptotic behavior of nonlinear diffusions

Asymptotic Behavior of Nonlinear Diffusions

for a given initial data u(x, 0) = u0(x) ≥ 0, where p > 1 and N ≥ 2. Such a solution exists and it is unique in the natural weak sense under rather mild conditions on u0. In particular, this is the case for u0 ∈ L , condition which we will assume in what follows. We refer the reader to [11,10] for general results on the issues of existence, uniqueness and regularity of non-negative solutions. I...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Long-time asymptotic expansions for nonlinear diffusions in Euclidean space∗

∗RJM acknowledges partial support of his research by Natural Sciences and Engineering Research Council of Canada Grant 217006-08. This material is based in part upon work supported by the National Science Foundation under Grant No. 0932078 000, while RJM was in residence at the Mathematical Science Research Institute in Berkeley, California, during the fall semester of 2014. c ©2014 by the auth...

Asymptotic Behavior Results for Nonlinear

This paper is focused on the following nonlinear impulsive neutral differential equation k 0 t t , t t 0, (t))) f(x(γ t q(t) (t))) f(x(β t p(t) ] t))) c(t)g(x(α([x(t) ≠ ≥ = − + ′ + 1,2,3,... k , f(x(s))ds s (s)) q(γ f(x(s))ds s (s)) p(β) a (1) x(t a) x(t k k k k t) γ(t 1 t) β(t 1 k k k k Sufficient conditions are obtained for every solution of (*) to tends to a constant as t → ∞.

asymptotic behavior of multivariate reward processes with nonlinear reward functions