Acta Applicandae Mathematicae最新文献

{"title":"A Unified Multifaceted Space-Time Wavelet Framework and Its Singularity Analysis for Weakly Singular Non-local Partial Integro-Differential Equations in High Dimensions","authors":"Sudarshan Santra,&nbsp;Pratibhamoy Das,&nbsp;Palle Jorgensen","doi":"10.1007/s10440-025-00756-4","DOIUrl":"10.1007/s10440-025-00756-4","url":null,"abstract":"<div><p>This work presents a comprehensive efficiency and convergence analysis of wavelet-based methods within a multi-dimensional framework for detecting singularities in nonlocal weakly singular integro-partial differential equations in one and two dimensions. The proposed approach incorporates the multi-resolution properties of wavelets to accurately identify and localize singularities in solutions to such equations. Combinations of space-time wavelets with their advantages are very limited for higher-dimensional problems, and their convergence analysis on collocation points is not fully clear till the present day. For problems having time singularity, the present work shows that multi-resolution analysis through 2D/3D Haar wavelets requires a lower regularity assumption for the convergence of the proposed procedure than several approaches on finite-difference setup or other wavelets like Hermite, Chebyshev, or Bernoulli’s wavelets. In particular, we produce a higher-order convergence result (second-order accurate) in the <span>(L^{2})</span> norm, based on sufficient regularity assumptions on the solution. In addition to the higher-order estimate, we provide the wavelet-based truncation error estimate for several terms, such as the time-fractional derivative, Volterra &amp; Fredholm integral operators, classical derivatives, and their effects on the regularity of the function for future researchers in this domain. Numerical tests are performed in the <span>(L^{2})</span> and <span>(L^{infty })</span> norms to compare the efficiency of this method over existing approaches for weakly singular nonlocal integro-partial differential equations. These experiments show the efficiency of the proposed approach in several kinds of regularity assumptions of the solution. This also guarantees the convergence of approximations to the functions having weak singularities in time and the higher-order accuracy for sufficiently smooth solutions.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"200 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00756-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Existence of the (H^{1}) Strong Solution to a Climate Dynamics Model with Horizontal Dissipation and Phase Transformation of Water Vapor","authors":"Ruxu Lian,&nbsp;Yue Hu,&nbsp;JieQiong Ma","doi":"10.1007/s10440-025-00752-8","DOIUrl":"10.1007/s10440-025-00752-8","url":null,"abstract":"<div><p>In this paper, we investigate the primitive three-dimensional dynamic equations for moist atmosphere with only horizontal dissipation. Especially, we introduce the phase transformation of water vapor, which are considered as some nonlinear functions related to temperature and pressure. For any <span>(H^{1})</span> initial data, the local well-posedness of strong solution can be established by decomposing velocity field into barotropic velocity field and baroclinic velocity field, as well as energy estimates method. Furthermore, applying logarithmic type Sobolev inequality, we can obtain the estimates of state functions in global time. Then the well-posedness of global strong solution can be proved.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"200 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and Oscillatory Dynamics in Fractional Ecological Models Using a Crossing Boundary Framework","authors":"Jesús Enrique Escalante-Martínez,&nbsp;Porfirio Toledo,&nbsp;José Alfredo Zavaleta-Viveros","doi":"10.1007/s10440-025-00750-w","DOIUrl":"10.1007/s10440-025-00750-w","url":null,"abstract":"<div><p>In this study, we delve into the dynamics of plant, pollinator, and herbivore interactions using fractional models, which effectively capture memory effects and intricate temporal dependencies that conventional integer-order models often overlook. A significant result is the numerical evidence of oscillatory dynamics induced by variations in the predator mortality parameter. Our findings reveal that the dynamics and stability of the system depend on the fractional order. In the classical case, a Hopf bifurcation emerges, accompanied by a limit cycle, in agreement with the existing literature. Moreover, analysis across different fractional orders shows similar behavior when a pair of complex eigenvalues crosses the Matignon sector, inducing a change in the equilibrium’s stability and producing oscillatory patterns. These insights offer valuable information on the parameters that drive ecosystem dynamics and contribute to a more comprehensive understanding of fractional system stability in ecological modeling.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"200 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Well-Posedness of Axisymmetric MHD Equations with Vertical Magnetic Diffusion and Nonzero Swirl","authors":"Fan Zhang","doi":"10.1007/s10440-025-00753-7","DOIUrl":"10.1007/s10440-025-00753-7","url":null,"abstract":"<div><p>The purpose of this paper is to study the incompressible MHD equations with vertical magnetic diffusion in <span>(mathbb{R}^{3})</span>. We establish the global well-posedness of the system if the initial data are axially symmetric and the swirl component of the initial velocity is sufficiently small.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"200 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local and Global Solvability in a Viscous Wave Equation Involving General Temperature-Dependence","authors":"Torben J. Fricke","doi":"10.1007/s10440-025-00751-9","DOIUrl":"10.1007/s10440-025-00751-9","url":null,"abstract":"<div><p>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 </p><div><div><span> $$begin{aligned} left { textstylebegin{array}{l} u_{tt} = (gamma (Theta ) u_{xt})_{x} + (tilde {gamma }(Theta ) u_{x})_{x}+(f( Theta ))_{x}, Theta _{t} = DTheta _{xx} + Gamma (Theta ) u_{xt}^{2}+F(Theta )u_{xt}, end{array}displaystyle right . end{aligned}$$ </span></div></div><p> in an open bounded interval, which with <span>(gamma equiv tilde {gamma }equiv Gamma )</span> as well as <span>(fequiv F)</span> 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 <span>(f)</span> and <span>(F)</span>, but also the core components <span>(gamma )</span>, <span>(tilde {gamma })</span> and <span>(Gamma )</span>, are dependent on the temperature variable <span>(Theta )</span>. Firstly, a statement regarding the local existence of classical solutions is derived for arbitrary <span>(D &gt; 0)</span>, <span>(0 &lt;gamma )</span>, <span>(tilde {gamma }in C^{2}([0,infty )))</span>, and <span>(0 le Gamma in C^{1}([0, infty )))</span>, for functions <span>(fin C^{2}([0,infty );mathbb{R}))</span> and <span>(Fin C^{1}([0,infty );mathbb{R}))</span> with <span>(F(0)=0)</span>, and for suitably regular initial data of arbitrary size. Secondly, if <span>(tilde{gamma } = acdot gamma +mu )</span>, with <span>(a&gt;0)</span> and arbitrary <span>(mu &gt;0)</span>, there exists <span>(delta &gt;0)</span> with the property that whenever in addition to the above we have </p><div><div><span>$$ frac{a}{gamma (Theta _{star })}le delta qquad text{and}qquad frac{|f'(Theta _{star })|cdot |F(Theta _{star })|}{Dcdot gamma (Theta _{star })} le delta , $$</span></div></div><p> for initial data close to the constant level given by <span>(u = 0)</span> and <span>(Theta =Theta _{star })</span>, with any fixed <span>(Theta _{star }ge 0)</span>, it is demonstrated that these solutions are indeed global in time and possess the property that <span>(u_{xt})</span>, <span>(u_{x})</span>, <span>(u_{xx})</span> and <span>(Theta _{x})</span> decay exponentially fast in <span>(L^{2})</span>. In this context, the parameter <span>(mu )</span> 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 <span>(L^{2})</span> spaces.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"200 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00751-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of Grazing Intensity and Non-local Delay on Vegetation Patterns in Semi-Arid Areas","authors":"Gaihui Guo,&nbsp;Tingting Wei,&nbsp;Fujie Jia,&nbsp;Haixia Li","doi":"10.1007/s10440-025-00749-3","DOIUrl":"10.1007/s10440-025-00749-3","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structural Similarity in Joint Inverse Problems","authors":"Teun Schilperoort,&nbsp;Tristan van Leeuwen","doi":"10.1007/s10440-025-00748-4","DOIUrl":"10.1007/s10440-025-00748-4","url":null,"abstract":"<div><p>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 <span>(W^{m,p})</span> and <span>(SBV)</span>. 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 <span>(N)</span> coupled problems is introduced.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00748-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison Principles and Asymptotic Behavior of Delayed Age-Structured Neuron Models","authors":"María J. Cáceres,&nbsp;José A. Cañizo,&nbsp;Nicolas Torres","doi":"10.1007/s10440-025-00746-6","DOIUrl":"10.1007/s10440-025-00746-6","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recovering the Diffusion Coefficient in the Porous Medium Equation from a Large-Time Measurement","authors":"Hagop Karakazian,&nbsp;Toni Sayah,&nbsp;Faouzi Triki","doi":"10.1007/s10440-025-00747-5","DOIUrl":"10.1007/s10440-025-00747-5","url":null,"abstract":"<div><p>This paper addresses the time-dependent Porous Medium Equation, <span>(u_{t} - alpha Delta u^{gamma }= 0)</span> with polytropic exponent <span>(gamma &gt;1)</span> and diffusion coefficient <span>(alpha &gt;0)</span>. Given the value of <span>(gamma )</span> and the solution <span>(u)</span> at a large time <span>(T)</span>, our goal is to determine the parameter <span>(alpha )</span> without the knowledge of the initial data <span>(u(0))</span>. Leveraging an asymptotic inequality satisfied by <span>(u(T))</span>, we propose a numerical algorithm to recover <span>(alpha )</span> through a minimization problem. Furthermore, we establish an upper bound on the error between the exact and recovered values of <span>(alpha )</span> and perform numerical simulations in two and three dimensional cases.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Final Value Problem for the Nonlinear Modified Helmholtz Equation Associated with the Nonlinear Wave Velocity","authors":"Long Pham Nguyen Hoang,&nbsp;Triet Le Minh,&nbsp;Phong Luu Hong,&nbsp;Hieu Phan Trung","doi":"10.1007/s10440-025-00745-7","DOIUrl":"10.1007/s10440-025-00745-7","url":null,"abstract":"<div><p>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 </p><div><div><span>$$triangle uleft ( x,yright ) -kleft ( l_{0}left ( uright ) left ( yright ) right ) uleft ( x,yright ) =Sleft ( x,y,uleft ( x,yright ) right ) ,~xin Omega ,~0&lt; y&lt; L. $$</span></div></div><p> 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.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}