Estimates for solutions of Burgers type equations and some applications

We obtain precise large time asymptotics for the Cauchy problem for Burgers type equations satisfying shock profile condition. The proofs are based on the exact a priori estimates for (local) solutions of these equations and a recent result of the first and second authors.Comment: to appear in J. Math. Pure et App

Technological changes on the macroeconomic level—mathematical modeling

We consider two of the technological changes on the macroeconomic level. The first type is due to changes of addresses of mutual deliveries between producers and the second type is due to technological progress

New conditions for the existence of equilibrium prices

We study the existence of equilibrium price vector in a supply-demand model taking into account the transaction costs associated with the sale of products. In this model, the demand function is the solution to the problem of maximizing the utility function under budget constraints. The supply function is the solution to the problem of maximizing the profit (with given transaction losses) on the technology set. We establish sufficient conditions for the existence of the equilibrium price vector, which are consequences of some theorems in the theory of covering mappings