We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings...

We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings...

We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings...

Motivated by time series analysis, we consider the problem of solving the recurrence relation un+1 = vn+1 +un⊗vn for n ≠ 0 and un, given the sequence vn. A solution is given as a Bell polynomial. When vn can be written as a weighted sum of nth powers, then the solution un also takes this form. Mathematical subject classification: 33E99.

Motivated by time series analysis, we consider the problem of solving the recurrence relation un+1 = vn+1 + un ⊗ vn for n ≠ 0 and un, given the sequence vn. A solution is given as a Bell polynomial. When vn can be written as a weighted sum of nth powers, then the solution un also takes this form. Mathematical subject classification: 33E99.

Let S be a semigroup of homeomorphisms of a compact metric space M and suppose that is a family of subsets of S. This paper gives a characterization of the -chain control sets as intersection of control sets for the semigroups generated by the neighborhoods of the subsets in . We also study the behavior of -chain control sets on principal bundles and their associated bundles.

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...

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...

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.

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...

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/ , 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 > ), we obtain that the temperature distribution...

We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a,b] Ì R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts...

This paper considers a pair of transmission problems for the system of piezoelectricity having piecewise constant coefficients. Under suitable monotonicity conditions on the coefficients and certain geometric conditions on the domain and the interfaces where the coefficients have a jump discontinuity, results on simultaneous boundary observation and simultaneous exact control are...