Abstract. The object of this paper is the uniqueness for a d-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so called Barenblatt solution of the fast diffusion equation which is the partial differential equation ∂tu = ∂ 2 xx u with m ∈ (0, 1)...

We extend Galor and Weil (2000) by including geographical factors in order to show that under some initial conditions, an economy may be locked in Malthusian stagnation and never take off. Specifically, we characterize the set of geographical factors for which this happens, and this way we show how the interplay of the available “land”, its suitability for living, and its degree of isolation, d...

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

We study the equation u̇ = log det(uαβ̄)−Au+f(z, t) in domains of C. This equation has a close connection with the Kähler-Ricci flow. In this paper, we consider the case where the boundary condition is smooth and the initial condition is irregular.

We study a simple model of factor saving technological innovation in a concave framework. Capital can be used either to reproduce itself or, at additional cost, to produce a higher quality of capital that requires less labor input. If higher quality capital can be produced quickly, we get a model of exogenous balanced growth as a special case. If, however, higher quality capital can be produced...

This paper presents a generalized Gronwall inequality with singularity. Using the inequality, we study the dependence of the solution on the order and the initial condition of a fractional differential equation. © 2006 Elsevier Inc. All rights reserved.

The paper assumes a continuum of two period-lived agents; agents are identical except for the inherited income. Young agents optimally allocate their inherited income between consumption and investment in human capital in a stochastic environment. In the second period they receive a wage proportional to the accumulated human capital and invest in o®spring. Two main results are provided: a low e...

Although a complete dynamic model includes the equations of motion as well as the initial conditions, many of the learning dynamics in the literature do not entail a serious theory of initial conditions. This paper explores and evaluates five approaches to complete learning models with a theory of initial conditions. We find that (1) the initial period’s fit is sensitive to the model of initial...

We present a model with an infinite volume bulk in which a braneworld with a cosmological constant evolves to a static, 4-dimensional Minkowski spacetime. This evolution occurs for a generic class of initial conditions with positive energy densities. The metric everywhere outside the brane is that of a 5-dimensional Minkowski spacetime, where the effect of the brane is the creation of a frame w...