We consider a nonlocal convection-diffusion equation , where J is a probability density. We supplement this equation with step-like initial conditions and prove the convergence of the corresponding solutions towards a rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the inviscid Burgers equation.
In this paper we explore a new model of field carcinogenesis, inspired by lung cancer precursor lesions, which includes dynamics of a spatially distributed population of pre-cancerous cells c(t, x), constantly supplied by an influx μ of mutated normal cells. Cell proliferation is controlled by growth factor molecules bound to cells, b(t, x). Free growth factor molecules g(t, x) are produced by precancerous cells and may diffuse before they become bound to other cells. The purpose of modelling is...
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of with damping terms of the form , where or . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when . For existence of smooth attractors is more complicated and follows...
This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into...
Dimostriamo l'esistenza della soluzione globale per un sistema di equazioni delle onde con nonlinearità quadratica dipendente dalle variabili spazio-tempo. Come in [3] la tecnica è basata sulla trasformazione di Penrose.
In the paper some solution properties of the Love's equation are compared with those of the classical wave equation for a certain class of boundary conditions. The method of small parameter is used.