Acta Applicandae Mathematicae最新文献

This paper presents an inverse problem of identifying two ionic parameters of a nonlocal reaction-diffusion system in cardiac electrophysiology modelling. We used a nonlocal FitzHugh-Nagumo monodomain model which describes the electrical activity in cardiac tissue with the diffusion rate assumed to depend on the total electrical potential in the heart. We established at first, the global Carleman estimate adapted to nonlocal diffusion to obtain our main result which is the uniqueness and the Lipschitz stability estimate for two ionic parameters ((k,gamma )).

Stochastic ultimate boundedness has always been a very important property, which plays an important role in the study of stochastic models. Thus, in this paper, we will study a stochastic periodic chemostat system, in which we assume that the nutrient input concentration and noise intensities are periodic. In order to make the stochastic periodic model have mathematical and biological significance, we will study a very important issue: the existence, uniqueness and ultimate boundedness of a global positive solution for a stochastic periodic chemostat system.

For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.

In this article, we consider two- and three- dimensional stochastic convective Brinkman-Forchheimer extended Darcy (CBFeD) equations

on a torus, where (mu ,beta >0), (alpha in mathbb{R}), (rin [1,infty )) and (qin [1,r)). The goal is to show that the solutions of 2D and 3D stochastic CBFeD equations driven by Brownian motion can be approximated by 2D and 3D stochastic CBFeD equations forced by pure jump noise/random kicks on the state space (mathrm{D}([0,T];mathbb{H})). For the cases (d=2), (rin [1,infty )) and (d=3), (rin (3,infty )), by using minimal regularity assumptions on the noise coefficient, the results are established for any (mu ,beta >0). For the case (d=r=3), the same results are obtained for (2beta mu geq 1).

In this paper we study the existence of positive solutions for the following Schrödinger–Maxwell system of singular elliptic equations

where (Omega ) is a bounded open set of (mathbb{R}^{N}, N>2), (r>1), (0 < theta <1) and (f) is nonnegative function belongs to a suitable Lebesgue space. In particular, we take advantage of the coupling between the two equations of the system by proving how the structure of the system gives rise to a regularizing effect on the summability of the solutions.

We are focused on solving a general class of bilevel variational inequalities involving quasimonotone operators in real Hilbert spaces. A strong convergent iterative method for solving the problem is presented and analysed. Our work generalizes several existing results in the literature and holds two major mathematical advantages. 1) Any generated sequence by the algorithm preserves the Fejér monotonicity property; and 2) There is no need to execute a line-search or know a-prior the strongly monotone coefficient or Lipschitz constant. Numerical experiments with comparisons to existing/related methods illustrate the performances of the proposed method and in particular, application to optimal control problems suggests the practical potential of our scheme.

This paper deals with the limiting behavior of nonlocal stochastic Schrödinger lattice systems with time-varying delays and multiplicative noise in weighted space. We first consider the existence and uniqueness of tempered pullback random attractors for considered stochastic system and then establish the upper-semicontinuity of these attractors when the length of time delay approaches zero.

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the classical (pi ) theorem to be restated in an explicit and precise form and its prerequisites to be clarified and relaxed. Augmented dimensional analysis, in contrast to classical dimensional analysis, is guaranteed to take into account all relations among the quantities involved. Several examples are given to show that the information thus gained, together with symmetry assumptions, can lead to new or stronger results. We also explore the connection between dimensional analysis and matroid theory, elucidating combinatorial aspects of dimensional analysis. It is emphasized that dimensional analysis rests on a principle of covariance.

In this paper, we study the long time behavior of solutions for an optimal control problem associated with the magnetic Bénard problem in a two dimensional bounded domain, achieved through the adjustment of distributed controls. We first construct a quasi-optimal solution for the magnetic Bénard problem characterized by exponential decay over time. We then derive preliminary estimates concerning the extended temporal behavior of all admissible solutions to the magnetic Bénard problem. Next we establish the existence of a solution for the optimal control problem over both finite and infinite time intervals. Additionally, we present the first-order necessary optimality conditions for the finite time interval case. Finally, we establish the long-time decay characteristics of the solutions for the optimal control problem.

This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads

with (sin (0, 1]). We are interested in solutions stemming from periodic positive bounded initial data. The given function (Fin mathcal{C}^{infty }(mathbb{R}^{+})) must satisfy (F'>0) a.e. on ((0, +infty )). For instance, all the functions (F(u)=u^{n}) with (nin mathbb{N}^{ast }) are admissible non-linearities. The local theory can also be developed on the whole space, however the most complete well-posedness result requires the periodic setting. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from positive data in (L^{infty }). We show that any weak solution is instantaneously regularized into (mathcal{C}^{infty }). We also describe the long-time asymptotics of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations, in particular (Ann. Fac. Sci. Toulouse, Math. 25(4):723–758, 2016; Ann. Fac. Sci. Toulouse, Math. 27(4):667–677, 2018).