Resumo em Inglês:

Exact solutions for the problem of drying with coupled phase change in a porous medium with a heat flux condition on x = 0 of the type - q0/ <img border=0 id="_x0000_i1026" src="../../../../../img/revistas/cam/v22n3/a01img01.gif" align=absmiddle>, with q0 > 0, for any value of the Luikov number Lu is obtained. This solution can be only obtained when q0 verifies a certain inequality. Besides, for large Luikov number (more precisely, Lu > <img border=0 id="_x0000_i1027" src="../../../../../img/revistas/cam/v22n3/a01img02.gif" align=absmiddle>), we obtain that the temperature distribution t2 reaches to a minimum value which is smaller than its initial temperature or limit value reached at +<FONT FACE=Symbol>¥</font>.

Resumo em Inglês:

This paper deals with a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and a microscopic phase parameter, which is related to the quantity of damaged material. The equilibrium equations are recovered by refining the principle of virtual powers including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behavior of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit.

Resumo em Inglês:

Berkovitz's notion of strategy and payoff for differential games is extended to study two player zero-sum infinite dimensional differential games on the infinite horizon with discounted payoff. After proving dynamic programming inequalities in this framework, we establish the existence and characterization of value. We also construct a saddle point for the game.

Resumo em Inglês:

We formulate conservation laws governing steam injection in a linear porous medium containing water. Heat losses to the outside are neglected. We find a complete and systematic description of all solutions of the Riemann problem for the injection of a mixture of steam and water into a water-saturated porous medium. For ambient pressure, there are three kinds of solutions, depending on injection and reservoir conditions. We show that the solution is unique for each initial data.

Resumo em Inglês:

In this work we study the variational inequality problem in finite dimensional spaces. The constraint set we consider has the structure of semi-infinite programming. Standard convergence analysis for outer approximation methods includes boundedness of the constraint set, or, alternatively, coerciveness of the data. Using recession tools, we are able to replace these assumptions by the hypotheses of boundedness of the solution set and that the domain of the operator contains the constraint set.

Resumo em Inglês:

Let S be a semigroup of homeomorphisms of a compact metric space M and suppose that <img border=0 id="_x0000_i1026" src="../../../../../img/revistas/cam/v22n3/a03img86.gif" align=absmiddle>is a family of subsets of S. This paper gives a characterization of the <img border=0 id="_x0000_i1027" src="../../../../../img/revistas/cam/v22n3/a03img86.gif" align=absmiddle>-chain control sets as intersection of control sets for the semigroups generated by the neighborhoods of the subsets in <img border=0 id="_x0000_i1028" src="../../../../../img/revistas/cam/v22n3/a03img86.gif" align=absmiddle>. We also study the behavior of <img border=0 id="_x0000_i1029" src="../../../../../img/revistas/cam/v22n3/a03img86.gif" align=absmiddle>-chain control sets on principal bundles and their associated bundles.