Asymptotic Analysis最新文献

{"title":"How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems","authors":"Guillaume Cantin","doi":"10.3233/asy-221818","DOIUrl":"https://doi.org/10.3233/asy-221818","url":null,"abstract":"In this paper, we study the asymptotic behaviour of the solutions to a degenerate reaction–diffusion system. This system admits a continuum of discontinuous stationary solutions due to the effect of a hysteresis process, but only one discontinuous stationary solution is compatible with a principle of preservation of locally invariant regions. Using a macroscopic mass effect which guarantees that fast particles help slow particles to displace, we establish a novel result of convergence of a non trivial set of trajectories towards a discontinuous pattern.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42232938","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":"Existence and convergence of the least energy sign-changing solutions for nonlinear Kirchhoff equations on locally finite graphs","authors":"Guofu Pan, Chao Ji","doi":"10.3233/asy-221819","DOIUrl":"https://doi.org/10.3233/asy-221819","url":null,"abstract":"In this paper, we study the least energy sign-changing solutions to the following nonlinear Kirchhoff equation − ( a + b ∫ V | ∇ u | 2 d μ ) Δ u + c ( x ) u = f ( u ) on a locally finite graph G = ( V , E ), where a, b are positive constants. We use the constrained variational method to prove the existence of a least energy sign-changing solution u b of the above equation if c ( x ) and f satisfy certain assumptions, and to show the energy of u b is strictly larger than twice that of the least energy solutions. Moreover, if we regard b as a parameter, as b → 0 + , the solution u b converges to a least energy sign-changing solution of a local equation − a Δ u + c ( x ) u = f ( u ).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47289591","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":"Existence, uniqueness, and asymptotic stability results for the 3-D steady and unsteady Navier–Stokes equations on multi-connected domains with inhomogeneous boundary conditions","authors":"J. Avrin","doi":"10.3233/asy-221816","DOIUrl":"https://doi.org/10.3233/asy-221816","url":null,"abstract":"We consider both stationary and time-dependent solutions of the 3-D Navier–Stokes equations (NSE) on a multi-connected bounded domain Ω ⊂ R 3 with inhomogeneous boundary values on ∂ Ω = Γ; here Γ is a union of disjoint surfaces Γ 0 , Γ 1 , … , Γ l . Our starting point is Leray’s classic problem, which is to find a weak solution u ∈ H 1 ( Ω ) of the stationary problem assuming that on the boundary u = β ∈ H 1 / 2 ( Γ ). The general flux condition ∑ j = 0 l ∫ Γ j β · n d S = 0 must be satisfied due to compatibility considerations. Early results on this problem including the initial results in (J. Math. Pures Appl. 12 (1933) 1–82) assumed the more restrictive flux condition ∫ Γ j β · n d S = 0 for each j = 1 , … , l. More recent results, of which those in (An Introduction to the Mathematical Theory of the Navier–Stokes Equations, vol. II 1994 Springer–Verlag) and (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) are particularly representative, assume only the general flux condition in exchange for size restrictions on the data. In this paper we also assume only the general flux condition throughout, and for virtually the same size restrictions on the data as in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) we obtain the existence of a weak solution that matches that found in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) when the assumptions imposed here and those assumed in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) are both met; additionally we demonstrate that this solution is unique. For slightly stronger size restrictions we obtain the existence and uniqueness of solutions of both Leray’s problem and global mild solutions of the corresponding time-dependent problem, while showing that both the stationary and time-dependent solutions we construct are a bit stronger than weak solutions. The settings in which we establish our results allow us to culminate our discussion by showing that our time-dependent solutions converge to each other exponentially in time, so that in particular our stationary solutions are asymptotically stable. We also discuss additional features which allow for data of increased size on certain domains, including those which are thin in a generalized sense.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45166456","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":"Controllability of a thermoelastic system","authors":"F. D. Araruna, A. Mercado, Luz de Teresa","doi":"10.3233/asy-221815","DOIUrl":"https://doi.org/10.3233/asy-221815","url":null,"abstract":"In this paper we present a null controllability result for a thermoelastic Rayleigh system. Instead of working directly with the control system, we obtain the controlled system as the modulus of elasticity in shear tends to infinity in the corresponding thermoelastic Mindlin–Timoshenko system. Our results follow the seminal book of Lagnese and Lions (Rech. Math. Appl. 6(1988)) where the controllability of a Kirkhhoff model is proposed as the limit of a controlled Mindlin–Timoshenko one. We use estimates for some eigenvalues of the beam model that were obtained in (SIAM J. Control Optim. 47 (2008) 1909–1938) and the recent paper of Komornik and Tenenbaum (Evolution Equations and Control Theory 4(3) (2015) 297–314) where explicit estimates for systems with real and complex eigenvalues are proposed.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48834737","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":"Singular behavior for a multi-parameter periodic Dirichlet problem","authors":"M. D. Riva, Paolo Luzzini, P. Musolino","doi":"10.3233/asy-231831","DOIUrl":"https://doi.org/10.3233/asy-231831","url":null,"abstract":"We consider a Dirichlet problem for the Poisson equation in a periodically perforated domain. The geometry of the domain is controlled by two parameters: a real number ϵ > 0, proportional to the radius of the holes, and a map ϕ, which models the shape of the holes. So, if g denotes the Dirichlet boundary datum and f the Poisson datum, we have a solution for each quadruple ( ϵ , ϕ , g , f ). Our aim is to study how the solution depends on ( ϵ , ϕ , g , f ), especially when ϵ is very small and the holes narrow to points. In contrast with previous works, we do not introduce the assumption that f has zero integral on the fundamental periodicity cell. This brings in a certain singular behavior for ϵ close to 0. We show that, when the dimension n of the ambient space is greater than or equal to 3, a suitable restriction of the solution can be represented with an analytic map of the quadruple ( ϵ , ϕ , g , f ) multiplied by the factor 1 / ϵ n − 2 . In case of dimension n = 2, we have to add log ϵ times the integral of f / 2 π.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48621729","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":"Stochastic fractional diffusion equations containing finite and infinite delays with multiplicative noise","authors":"N. Tuan, T. Caraballo, Tran Ngoc Thach","doi":"10.3233/asy-221811","DOIUrl":"https://doi.org/10.3233/asy-221811","url":null,"abstract":"In this work, we investigate stochastic fractional diffusion equations with Caputo–Fabrizio fractional derivatives and multiplicative noise, involving finite and infinite delays. Initially, the existence and uniqueness of mild solution in the spaces C p ( [ − a , b ] ; L q ( Ω , H ˙ r ) ) ) and C δ ( ( − ∞ , b ] ; L q ( Ω , H ˙ r ) ) ) are established. Next, besides investigating the regularity properties, we show the continuity of mild solutions with respect to the initial functions and the order of the fractional derivative for both cases of delay separately.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42088395","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":"On elliptic problems with Choquard term and singular nonlinearity","authors":"D. Choudhuri, Dušan D. Repovš, K. Saoudi","doi":"10.3233/ASY-221812","DOIUrl":"https://doi.org/10.3233/ASY-221812","url":null,"abstract":"Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded a.e. in the domain Ω and is Hölder continuous.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46894450","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":"Nonlinear fractional damped wave equation on compact Lie groups","authors":"Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal","doi":"10.3233/asy-231842","DOIUrl":"https://doi.org/10.3233/asy-231842","url":null,"abstract":"In this paper, we deal with the initial value fractional damped wave equation on G, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on G. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, i.e., damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44679698","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 note on local energy decay results for wave equations with a potential","authors":"R. Ikehata","doi":"10.3233/asy-231835","DOIUrl":"https://doi.org/10.3233/asy-231835","url":null,"abstract":"In this paper, we derive uniform local energy decay results for wave equations with a short-range potential in an exterior domain. In this study, we considered this problem within the framework of non-compactly supported initial data, unlike previously reported studies. The essential parts of analysis are both L 2 -estimates of the solution itself and the weighted energy estimates. Only a multiplier method is used, and we do not rely on any resolvent estimates.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43801409","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":"“Gradient-free” diffuse approximations of the Willmore functional and Willmore flow","authors":"Nils Dabrock, Sascha Knuttel, M. Roger","doi":"10.3233/ASY-221810","DOIUrl":"https://doi.org/10.3233/ASY-221810","url":null,"abstract":"We introduce new diffuse approximations of the Willmore functional and the Willmore flow. They are based on a corresponding approximation of the perimeter that has been studied by Amstutz-van Goethem [Interfaces Free Bound. 14 (2012)]. We identify the candidate for the Γ-convergence, prove the Γ-limsup statement and justify the convergence to the Willmore flow by an asymptotic expansion. Furthermore, we present numerical simulations that are based on the new approximation.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48417407","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}