Acta Applicandae Mathematicae最新文献

In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.

This paper investigates common variational inclusion problems (CVIPs) beyond the traditional inverse strongly monotone setting, focusing instead on a broader class of monotone and Lipschitz continuous operators. We introduce a novel two-step inertial algorithm incorporating self-adaptive regularization and relaxation techniques to address this generalized framework. We establish the strong convergence of the proposed method under mild assumptions. Extensive numerical experiments demonstrate that our algorithm consistently outperforms several existing approaches. Furthermore, we highlight the practical significance of our framework by reformulating a range of real-world applications, such as the elastic net in statistical learning, sparse logistic regression, and LASSO, as instances of CVIPs.

The following chemotaxis-consumption problem with no-flux boundary conditions has been considered

within a smoothly bounded domain (Omega subset mathbb{R}^{n}(ngeq 3)), where the parameters (kappa >beta >1), (alpha , gamma ,eta >0), and (T_{max }in (0,infty ]). This paper mainly examines the effects of nonlinear dissipation and nonlocal logistic feedback on solutions. Specifically, for all suitably regular initial data, it has been established that if

or

then the above system has a global classical solution. Compared with previous research results, the novelty (or difficulty) of this paper lies in the combination of non-local terms and nonlinear dissipation.

This paper is addressed to study asymptotic behavior for the Korteweg-de Vries equation with rapid oscillations, namely, the Korteweg-de Vries equation with rapidly oscillating potential and rapidly oscillating boundary force. In order to describe its asymptotic behavior, we establish the averaging principle for this system, this is important from both physical and mathematical standpoints. More precisely, two kinds of averaging principle is established, one is Bogoliubov first averaging principle for the Korteweg-de Vries equation on a finite time interval, the other is the Bogoliubov second averaging principle for the Korteweg-de Vries equation on the entire axis.

Exploring a more than 70 years old idea about the minimization of the spectral abscissa of linear functional differential equations, a series of recent works highlighted the insights that multiple spectral values may bring in the characterization of the decay rate for the solution of such dynamical systems. In fact, it has been shown that a spectral value of sufficiently high multiplicity tends to be dominant, in what is now known as the multiplicity-induced-dominancy (MID) property. When it is valid, this property can be remarkably helpful in the control of dynamical systems governed by functional differential equations or even some classes of partial differential equations. Beyond its simplicity, what sets it apart from other control methods is the valuable quantitative advantage it provides by prescribing the exact solution’s decay rate. Since then, many works have been dedicated to studying the extent of the MID as well as its use in practical control applications. In this paper, apart from the extension of the MID property to continuous-time difference functional equations with multiple delays, we study the case when the MID fails. In fact, despite the invalidity of the MID property, we emphasize the interest of forcing a spectral value multiplicity to derive a sharp estimate of the corresponding rightmost spectral value. To demonstrate the effectiveness of the proposed methodology, we consider the stabilization problem of the wave equation with an auto-regressive boundary feedback. By using an appropriate finite element modeling, a numerical simulation of the boundary control for the wave equation case is performed to illustrate these results through the example of vibration control of a long drill pipe submitted to a shock-like disturbance. The time responses show the effectiveness of the proposed approach and mainly that the decay rate can be arbitrarily selected.

This paper studies the asymptotic behavior of solutions to the non-autonomous Newton-Boussinesq equation defined on a two-dimensional unbounded Poincaré domain. Based on the well-posedness of solutions in (L^{2}(mathcal{O}) times L^{2}(mathcal{O})), we construct a continuous non-autonomous dynamical system in this space and prove the existence of a unique tempered pullback attractor. Moreover, under the assumption that the time-dependent external forces converge to time-independent fnctions as time approaches positive or negative infinity, we establish the asymptotically autonomous upper semicontinuity of the attractors. The main difficulty arising from the lack of compact Sobolev embeddings on unbounded domains is overcome by deriving uniform tail estimates for the solutions.

This paper is dedicated to the long-time behavior of a system of coupled one-dimensional wave equations modeling helicoidal flows of Maxwell fluid. In a scenario featuring nonlinear damping and source terms of arbitrary polynomial growth, we prove the existence of smooth finite dimensional global attractors as well as exponential attractors. We also prove that its long-time dynamics is completely determined by a finite set of linear continuous functionals.

In this paper, we study a quantitative refinement of a classical symmetrisation result for first-order Hamilton-Jacobi equations. We prove that the deficit in the comparison result, established by Giarrusso and Nunziante, controls both the asymmetry of the domain and the deviation of the solution and data from radial symmetry. This yields a stability version of the Giarrusso-Nunziante inequality.

In this paper, we apply Picard’s method to solve fractal differential equations arising in both ordinary and partial forms. We begin with a brief review of fractal calculus and introduce the Fractal Picard Iteration Method. This method is then used to solve ordinary and partial fractal differential equations systematically. As applications, we demonstrate the effectiveness of the approach by solving the fractal model of an RL circuit and the Schrödinger equation for a free particle. The results highlight the adaptability and strength of Picard’s method in addressing problems within fractal frameworks.

This paper investigates a contact and friction problem involving two electro-elastic bodies that interact with an electrically conductive foundation. The proposed model incorporates Signorini contact conditions with friction, non-homogeneous Neumann boundary conditions for non-contact zones and Robin boundary conditions for mechanical displacement. The resulting weak variational formulation is a system of nonlinear quasi-variational inequality and variational equality. The existence of solutions is established using fixed-point theory, and uniqueness is guaranteed under a smallness condition that relates the mechanical and electrical properties.