A Dynamic Model of Unemployment with Migration and Delayed Policy Intervention

The purpose of this paper is to build and analyse a model of unemployment, where jobs search is open to both natives and migrant workers. Markets and government intervention respond jointly to unemployment when creating new jobs. Full employment of resources is the focal point of policy action, stimulating vacancy creation. We acknowledge that policy is implemented with delays, and capture labour market outcomes by building a non-linear dynamic system. We observe jobs separation and matching, and extend our model to an open economy with migration and delayed policy intervention meant to reduce unemployment. We analyse the stability behaviour of the resulting equilibrium for our dynamic system, including models with Dirac and weak kernels. We simulate our model with alternative scenarios, where policy action towards jobs creation considers both migration and unemployment, or just unemployment

Estimates of blow-up time for a non-local problem modelling an Ohmic heating process

We consider an initial boundary value problem for the non-local equation, ut = uxx+λf(u)/(∫1-1f (u)dx)2, with Robin boundary conditions. It is known that there exists a critical value of the parameter λ, say λ*, such that for λ &gt; λ* there is no stationary solution and the solution u(x, t) blows up globally in finite time t*, while for λ &lt; λ* there exist stationary solutions. We find, for decreasing f and for λ &gt; λ*, upper and lower bounds for t*, by using comparison methods. For f(u) = e−u, we give an asymptotic estimate: t* ∼ tu(λ−λ*)−1/2 for 0 &lt; (λ−λ*) [Lt ] 1, where tu is a constant. A numerical estimate is obtained using a Crank-Nicolson scheme.</jats:p