Applied Mathematics and Optimization

We are concerned in the present work with diverse perturbations of time dependent monotone/accretive evolution. New applications such as integral–differential Volterra perturbation, periodicity, relaxation, asymptotic properties are presented.

In this work, we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belong to the fixed point set of an ...

We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in ...

This work studies a class of chemotaxis systems generalizing the prototype $$\begin{array}{c}\hfill \left\{\begin{array}{c}{\displaystyle u_t=d\mathrm{\nabla }·({(1+u)}^{m-1}\mathrm{\nabla }u)-\chi \mathrm{\nabla }·(u{(1+u)}^{\sigma -2}\mathrm{\nabla }v)+\mu u^{\alpha }(1-{\int }_{\mathrm{\Omega }}{u}^{\beta }),}\hfill \\ 0=\mathrm{\Delta }v-v+u,\hfill \end{array}\right)\end{array}$$with nonnegative initial data under zero-flux boundary conditions in a smooth bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^N$$(N\ge 1)$, where d, m, ...$$$\mathrm{}$$\mathrm{}$$$$\mathrm{}$$$\begin{array}{c}\hfill {\displaystyle \frac{}{\mathrm{}}\frac{\mathrm{}}{}}\end{array}$$${\displaystyle \frac{}{\mathrm{}}}$$$

The main purpose of this paper is to apply the notion of hierarchical control to a coupled degenerate non linear parabolic equations. We use the Stackelberg–Nash strategy with one leader and two followers. The followers solve a Nash equilibrium ...

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary ...

In this paper, a three-layer Rao–Nakra sandwich beam is considered where the core viscoelastic layer is constrained by the purely elastic or piezoelectric outer layers. In the model, uniform bending motions of the overall laminate are coupled to ...

In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms ...

The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application of both the forward linear operator and its ...

We present a complete characterization of the (uniform) exponential stabilization for a class of viscoelastic models under small delay perturbations. The main ingredient under consideration is the notion of admissible kernels. While in the ...

In this paper, we investigate the stabilization of a one-dimensional piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge conditions, we reformulate our system to achieve the existence and uniqueness of the ...

In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow containers: symmetric canals with a given free surface width and ...$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}\mathrm{}$$\mathrm{}$

We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_{\nu }$, on the set of probability measures $\mathcal{P}(X)$ on a domain $X\subseteq {\mathbb{R}}^m$. This metric is based on a slight refinement of the notion of generalized geodesics with ...$$$$$$$$$$${}_{}$$$$$$$$$$$$$$$${\mathbb{}}^{}$$$$$$$$$

In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from (Lasiecka et al. in Nonlinear Anal 44:54–85, 2018). An elastic body surrounded by a liquid in a ...

We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we provide conditions for the existence of a Nash equilibrium ...

In this paper we deal with a class of nonlinear quasi-variational inequalities involving a set-valued map and a constraint set. First, we prove that the set of weak solutions of the inequality is nonempty, weakly compact and upper semicontinuous ...

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results. Then, we ...

This paper is concerned with the relationship between the maximum principle and dynamic programming for a large class of optimal control problems with maximum running cost. Inspired by a technique introduced by Vinter in the 1980s, we are able to ...

In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential equations and show that, in ...

We establish the existence and uniqueness of viscosity solutions to the weakly coupled second-order parabolic Hamilton–Jacobi–Bellman equations under Hölder continuous condition, for which the standard quasi-monotone condition does not hold. The ...