The aim of this paper is to investigate the existence of optimal controls for systems described by stochasticpartial differential equations (SPDEs) with locally monotone coefficients controlled by external forces whichare feedback controls. To attain our objective we adapt the argument of Lisei (2002) where the existence ofoptimal controls to the stochastic Navier–Stokes equation was studied. The results obtained in the presentpaper may be applied to demonstrate the existence of optimal controls to various types of controlledSPDEs such as: a stochastic nonlocal equation and stochastic semilinear equations which are locally monotone equations; we also apply the result to a monotone equation such as the stochastic reaction–diffusionequation and to a stochastic linear equation.

In this paper we study the distributed problem for the two-dimensional mathematical model of the invasion of a healthy tissue by a generic solid tumor that has been vascularized, due to coupled parabolic systems. We prove the existence, uniqueness, and local null controllabilty.

In this paper, we prove that if the initial data is small enough, we obtain an explicit L∞(QT)‐estimate for a two‐dimensional mathematical model of cancer invasion, proving an explicit bound with respect to time T for the estimate of solutions.

The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are feedback controls. We apply our result to various types of SPDEs such as the stochastic 2-D Navier-Stokes equation, the stochastic nonlocal equation, stochastic linear equations and stochastic semilinear equations.

In this paper we study the distributed optimal control problem for the two-dimensional mathematical model of cancer invasion. Existence of optimal state-control and stability is proved and an optimality system is derived.

In this article we investigate the existence and uniqueness of weak solutions for a stochastic nonlinear parabolic coupled system of reaction-diffusion of nonlocal type, and with multiplicative white noise. An important result on the asymptotic behavior of the weak solutions is presented as well.

In this article we investigate the existence and uniqueness of weak solutions for a stochastic nonlinear parabolic coupled system of reaction-diffusion of nonlocal type, and with multiplicative white noise. An important result on the asymptotic behavior of the weak solutions is presented as well.

The existence and uniqueness of weak solutions for a random version of a class ofnonlinear parabolic problems of nonlocal type with additive noise are studied.

In this paper we are concerned with some theoretical questions forthe FitzHugh-Nagumo equation. First, we recall the system, we briefly explain the meaning of the variables and we present a simple proof of the existence and uniqueness of strong solution. We also consider an optimal control problem for this system. In this context, the goal is to determine how can we act on the system in order to get good properties. We prove the existence of optimal state-control pairs and, as an application of the Dubovitski-Milyoutin formalism, we deduce the corresponding optimality system. We also connect the optimal control problem with a controllability question and we construct a sequence of controls that produce solutions that converge strongly to desired states. This provides a strategy to make the system behave as desired. Finally, we present some open questions related to the control of this equation.

This article studies the existence of weak solutions for a stochastic version of the FitzHugh-Nagumo equations in a time dependent domain Q, where Q is a image of a cylinder C of Rn.

This article studies the existence of weak solutions for a stochastic version of the FtzHugh-Nagumo equations. The random elements are introduced through initial values and forcing terms of associated Cauchy problem, which may be white noise in the time. Moreover there is a dependence of a stochastic  parameter.

Apresentamos um modelo matemático para a metapsicologia proposta por Freud em seu trabalho conhecido como o Projeto para uma Psicologia Científica . O modelo é consequência de uma associação entre os três arquétipos da Física-Matemática e os três sistemas neurais propostos por Freud.

Si presenta un risultato di regolarità per un sistema non lineare di equazioni di Klein-Gordon con esponenti di Sobolev critici.