Acta Applicandae Mathematicae最新文献

The present manuscript studies a coupled thermoelastic-viscoelastic system, modelling the interaction between mechanical displacement and temperature in viscoelastic materials in a bounded interval. This topic is of interest in the fields of applied mathematics and continuum mechanics. The system under consideration reads

in an open bounded interval, which with (gamma equiv tilde {gamma }equiv Gamma ) as well as (fequiv F) reduces to the classical model for the evolution of strains and temperatures in thermoviscoelasticity. In contrast to the preceding related studies, the present study focuses on situations in which not only (f) and (F), but also the core components (gamma ), (tilde {gamma }) and (Gamma ), are dependent on the temperature variable (Theta ). Firstly, a statement regarding the local existence of classical solutions is derived for arbitrary (D > 0), (0 <gamma ), (tilde {gamma }in C^{2}([0,infty ))), and (0 le Gamma in C^{1}([0, infty ))), for functions (fin C^{2}([0,infty );mathbb{R})) and (Fin C^{1}([0,infty );mathbb{R})) with (F(0)=0), and for suitably regular initial data of arbitrary size. Secondly, if (tilde{gamma } = acdot gamma +mu ), with (a>0) and arbitrary (mu >0), there exists (delta >0) with the property that whenever in addition to the above we have

for initial data close to the constant level given by (u = 0) and (Theta =Theta _{star }), with any fixed (Theta _{star }ge 0), it is demonstrated that these solutions are indeed global in time and possess the property that (u_{xt}), (u_{x}), (u_{xx}) and (Theta _{x}) decay exponentially fast in (L^{2}). In this context, the parameter (mu ) captures the weak inclusion of the electric field within the system. This aspect constitutes the primary novel contribution of the present analysis. The aforementioned results are obtained by detecting suitable dissipative properties of functionals involving norms of these gradients in (L^{2}) spaces.

In semi-arid areas, grazing intensity has a certain impact on vegetation, and the non-local interaction of roots in absorbing water also plays an indispensable role in vegetation. So in this paper, a vegetation-water model considering grazing intensity and non-local delay is established. The conditions for Turing patterns occurrence in the vegetation-water model are determined through an analytical method. Additionally, the multiple-scale analysis is employed to get the amplitude equations at the critical value of Turing bifurcation. Through the stability analysis of amplitude equations, we determine the conditions for the emergence of different Turing patterns. Various spatial distributions of vegetation in the semi-arid areas are qualitatively described by numerical simulations. The intensification of grazing intensity will change the structural arrangement of vegetation patterns: spot patterns → mixed patterns → stripe patterns. The results indicate that the overall trend of vegetation growth would be better with the increase of grazing intensity. Besides, we demonstrate that the non-local interaction between vegetation and water plays a key role in the formation of vegetation patterns, offering a theoretical foundation for the conservation and restoration of vegetation.

Joint inverse problems occur in many practical situations, where different modalities are used to image the same object. Structural similarity is a way to regularize such joint inverse problems by imposing similarity between the images. While structural similarity has found widespread use in many practical settings, its theoretical foundations remain underexplored. This study develops an over-arching formulation for these types of problems and studies their well-posedness via the Direct Method from the calculus of variations. We focus in particular on lower semi-continuity and coerciveness as essential properties for the well-posedness of the variational problem in (W^{m,p}) and (SBV). Here quasiconvexity and growth properties of the structural similarity quantifier turns out to be essential. We find that the use of gradient-difference, cross-gradient or Schatten norms as structural similarity quantifiers is theoretically justified. A generalized form of the cross-gradient that inherently works on (N) coupled problems is introduced.

In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last discharge, with many interesting dynamics depending on the type of interactions between neurons. We investigate the asymptotic behavior of this equation in the case of both discrete and distributed delays that account for the time needed to transmit a nerve impulse from one neuron to the rest of the ensemble. To prove the convergence to the equilibrium, we follow an approach based on comparison principles for Volterra equations involving the total activity, which provides a simpler and more straightforward alternative technique than those in the existing literature on the elapsed-time model.

This paper addresses the time-dependent Porous Medium Equation, (u_{t} - alpha Delta u^{gamma }= 0) with polytropic exponent (gamma >1) and diffusion coefficient (alpha >0). Given the value of (gamma ) and the solution (u) at a large time (T), our goal is to determine the parameter (alpha ) without the knowledge of the initial data (u(0)). Leveraging an asymptotic inequality satisfied by (u(T)), we propose a numerical algorithm to recover (alpha ) through a minimization problem. Furthermore, we establish an upper bound on the error between the exact and recovered values of (alpha ) and perform numerical simulations in two and three dimensional cases.

This study focuses on the development and analysis of the backward problem for the nonlinear modified Helmholtz equation associated with nonlinear wave velocity. The governing equation is given as follows

To overcome the ill-posseness of the above problem, we apply the variational quasi-reversibility method. It is imperative to investigate the convergence analysis of this regularization method when we do not determine a formula of the exact solution. In this regard, we construct the approximate problem by adding the so-called perturbing operator to the original problem and by exploiting the Fourier reconstructed the final data. Then, we obtain the Hölder convergence rate of the proposed scheme under some certain assumptions on the exact solution. Finally, a numerical example is provided to corroborate the theoretical results.

This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.

One of the popular generalizations of the classical notion of essential spectra is the notion of pseudo essential spectra. The study around such notion has gained intensive interest in many research fields, particularly, in the theory of Fredholm operators. So, the novelty of our work is to develop a new sufficient criteria linked to the notion of (Phi )-perturbation function (recently invested by M. Mebekhta in (J. Oper. Theory 51:3–18, 2004)) allowing us to derive some new spectral analysis of some sets of (varepsilon )-pseudo Fredholm operators and their corresponding pseudo Weyl essential spectra. Moreover, our aim comes also to reach a new characterization in the setting of the so-called pseudo Weyl essential spectrum of a closed densely defined operator via the above approach of perturbation. Our results in this paper generalize and refine earlier work, particularly, the work done by S. Charfi et al. (Indag. Math. 28(3):670–679, 2017).

Environmental factors such as temperature, rainfall, and vegetation index play a crucial role in the transmission dynamics of malaria. Accurately quantifying the complex relationships between these variables and the malaria burden poses a significant challenge. In this study, we developed a host-mosquito mathematical model to investigate the impact of temperature, rainfall, and normalized difference vegetation index (NDVI) on malaria transmission dynamics calibrated with the Burundi case’s study. Mathematical analysis explored the equilibria, stability, and computation of the model’s threshold values. Numerical simulations suggest that temperature, rainfall, and vegetation index affect the transmission dynamics of malaria. Temperature and NDVI appear to exhibit a more pronounced influence among these factors. The conditions conducive to malaria transmission include a mean monthly temperature range of [20-25 °C], an averaged monthly NDVI range of approximately [0.4-0.6]. The reproduction number was used as a quantitative measure to predict the impact of temperature, rainfall, and NDVI on malaria transmission dynamics across Burundi. The results suggest a progressive increase in the reproduction number over time, suggesting a threat of the rising number of cases in Burundi if drastic control measures are not implemented.

In the present work, we are mainly concerned with some estimates related to the energy functional, in particular some uniform estimates of the solution decay rates. In this sense, we study the stable asymptotic behavior in terms of natural energy associated with the solution of a new class of fractional quasilinear hyperbolic equations with variable sources.