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Singular elliptic problem involving a Hardy potential and lower order term 涉及Hardy势和低阶项的奇异椭圆问题
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-03-09 DOI: 10.3233/asy-231832
A. Sbai, Y. El hadfi, Mounim El Ouardy
{"title":"Singular elliptic problem involving a Hardy potential and lower order term","authors":"A. Sbai, Y. El hadfi, Mounim El Ouardy","doi":"10.3233/asy-231832","DOIUrl":"https://doi.org/10.3233/asy-231832","url":null,"abstract":"We consider the following non-linear singular elliptic problem (1) − div ( M ( x ) | ∇ u | p − 2 ∇ u ) + b | u | r − 2 u = a u p − 1 | x | p + f u γ in  Ω u > 0 in  Ω u = 0 on  ∂ Ω , where 1 < p < N; Ω ⊂ R N is a bounded regular domain containing the origin and 0 < γ < 1, a ⩾ 0 , b > 0 , 0 ⩽ f ∈ L m ( Ω )  and  1 < m < N p . The main goal of this work is to study the existence and regularizing effect of some lower order terms in Dirichlet problems despite the presence of Hardy the potentials and the singular term in the right hand side.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42479028","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}
引用次数: 1
D s , 2 ( R N ) versus C ( R N ) local minimizers D s，2（RN）与C（RN）局部极小值
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-03-07 DOI: 10.3233/asy-231833
V. Ambrosio
{"title":"D s , 2 ( R N ) versus C ( R N ) local minimizers","authors":"V. Ambrosio","doi":"10.3233/asy-231833","DOIUrl":"https://doi.org/10.3233/asy-231833","url":null,"abstract":"Let s ∈ ( 0 , 1 ), N > 2 s and D s , 2 ( R N ) : = { u ∈ L 2 s ∗ ( R N ) : ‖ u ‖ D s , 2 ( R N ) : = ( C N , s 2 ∬ R 2 N | u ( x ) − u ( y ) | 2 | x − y | N + 2 s d x d y ) 1 2 < ∞ } , where 2 s ∗ : = 2 N N − 2 s is the fractional critical exponent and C N , s is a positive constant. We consider functionals J : D s , 2 ( R N ) → R of the type J ( u ) : = 1 2 ‖ u ‖ D s , 2 ( R N ) 2 − ∫ R N b ( x ) G ( u ) d x , where G ( t ) : = ∫ 0 t g ( τ ) d τ, g : R → R is a continuous function with subcritical growth at infinity, and b : R N → R is a suitable weight function. We prove that a local minimizer of J in the topology of the subspace V s : = { u ∈ D s , 2 ( R N ) : u ∈ C ( R N )  with  sup x ∈ R N ( 1 + | x | N − 2 s ) | u ( x ) | < ∞ } must be a local minimizer of J in the D s , 2 ( R N )-topology.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44010650","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}
引用次数: 0
Divergent sequence of nontrivial solutions for superlinear double phase problems 超线性双相问题非平凡解的发散序列
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-03-06 DOI: 10.3233/asy-231830
Nikolaos S. Papageorgiou, C. Vetro, F. Vetro
{"title":"Divergent sequence of nontrivial solutions for superlinear double phase problems","authors":"Nikolaos S. Papageorgiou, C. Vetro, F. Vetro","doi":"10.3233/asy-231830","DOIUrl":"https://doi.org/10.3233/asy-231830","url":null,"abstract":"We consider a double phase (unbalanced growth) Dirichlet problem with a Carathéodory reaction f ( z , x ) which is superlinear in x but without satisfying the AR-condition. Using the symmetric mountain pass theorem, we produce a whole sequence of distinct bounded solutions which diverge to infinity.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43753457","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}
引用次数: 0
Global solutions to coupled (Navier-)Stokes Newton systems in R 3 三维耦合(Navier-)Stokes - Newton系统的全局解
4区 数学
Asymptotic Analysis Pub Date : 2023-03-02 DOI: 10.3233/asy-221790
M. Hillairet, L. Sabbagh
{"title":"Global solutions to coupled (Navier-)Stokes Newton systems in R 3","authors":"M. Hillairet, L. Sabbagh","doi":"10.3233/asy-221790","DOIUrl":"https://doi.org/10.3233/asy-221790","url":null,"abstract":"We consider the motion of spherical particles in the whole space R 3 filled with a viscous fluid. We show that, when modelling the fluid behavior with an incompressible Stokes system, solutions are global and no collision occurs between the spheres in finite time.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135383663","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}
引用次数: 0
Asymptotic method and transient terms in exact controls 精确控制的渐近方法和暂态项
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-02-08 DOI: 10.3233/asy-231829
P. Destuynder
{"title":"Asymptotic method and transient terms in exact controls","authors":"P. Destuynder","doi":"10.3233/asy-231829","DOIUrl":"https://doi.org/10.3233/asy-231829","url":null,"abstract":"There is a narrow but hidden link between optimal control theory and the so-called Tikhonov regularization method. In fact, the small coefficient representing the marginal cost of the control can be interpreted as the regularization parameter in a Tikhonov method as far as there exists an exact control. This strategy enables one to adjust the cost function in the optimal control model in order to define the exact control which minimizes a given functional involving both the control but also the state variables during the control process. The goal of this paper is to suggest a method which gives a simple way to characterize and compute the exact control corresponding to the minimum of a given cost functional as said above. It appears as an extension of the phase control which is a finite dimensional version of the HUM control of J.L. Lions but for partial differential equations.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44561125","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}
引用次数: 0
Polynomial stabilization for thermoelastic Reissner–Mindlin–Timoshenko plates with structural damping 具有结构阻尼的热弹性Reissner–Mindlin–Timoshenko板的多项式镇定
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-23 DOI: 10.3233/asy-231826
A. Ramos, A. Araujo, A. Campelo, M. Freitas, L. S. Veras
{"title":"Polynomial stabilization for thermoelastic Reissner–Mindlin–Timoshenko plates with structural damping","authors":"A. Ramos, A. Araujo, A. Campelo, M. Freitas, L. S. Veras","doi":"10.3233/asy-231826","DOIUrl":"https://doi.org/10.3233/asy-231826","url":null,"abstract":"In this paper, we are interested in studying the well-posedness, optimal polynomial stability, and the lack of exponential stability for a class of thermoelastic system of Reissner–Mindlin–Timoshenko plates with structural damping, that is, with the dissipation of Kelvin–Voigt type on the equations for the rotation angles. We also consider the thermal effect with thermal variables described by Fourier’s law of heat conduction.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41340939","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}
引用次数: 0
Optimal control of a model for brain lactate kinetics 脑乳酸动力学模型的最优控制
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-09 DOI: 10.3233/asy-221823
Hussein Raad, L. Cherfils, C. Allery, R. Guillevin
{"title":"Optimal control of a model for brain lactate kinetics","authors":"Hussein Raad, L. Cherfils, C. Allery, R. Guillevin","doi":"10.3233/asy-221823","DOIUrl":"https://doi.org/10.3233/asy-221823","url":null,"abstract":"The aim of this paper is to first study a Cahn-Hilliard model for brain lactate kinetics with a control function. This control allows for optimal treatment administered to ill patients suffering from glioma, in order to reduce their brain lactate concentrations, and thereby to slow down the tumor growth. We establish the well-posedness of the problem and the continuity of the control-to-state mapping, the existence of a minimizer of the objective functional, and its Fréchet differentiability in suitable Banach spaces with respect to the control and with respect to time. Moreover, we derive the first-order necessary conditions that an optimal control has to satisfy. In the second part of the paper, we illustrate our theoretical results with numerical simulations using MRI data from the University Hospital of Poitiers.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41880950","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}
引用次数: 1
Cahn–Hilliard equation with regularization term 带正则化项的Cahn-Hilliard方程
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-03 DOI: 10.3233/asy-221821
Rim Mheich
{"title":"Cahn–Hilliard equation with regularization term","authors":"Rim Mheich","doi":"10.3233/asy-221821","DOIUrl":"https://doi.org/10.3233/asy-221821","url":null,"abstract":"We will study in this article the nonlinear Cahn–Hilliard equation with proliferation and regularization terms with regular and logarithmic potentials. First, we consider the regular potential case, we show that the solutions blow up in finite time or exist globally in time. Furthermore, we prove that the model possess a global attractor. In addition, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. In the second part, we consider the logarithmic potential case and show the existence of a global solution.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46091030","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}
引用次数: 0
How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems 磁滞如何在简并反应-扩散系统中产生不连续模式
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-12-09 DOI: 10.3233/asy-221818
Guillaume Cantin
{"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":" ","pages":""},"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}
引用次数: 0
Existence and convergence of the least energy sign-changing solutions for nonlinear Kirchhoff equations on locally finite graphs 局部有限图上非线性Kirchhoff方程最小能量变符号解的存在性与收敛性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-12-09 DOI: 10.3233/asy-221819
Guofu Pan, Chao Ji
{"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":" ","pages":""},"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}
引用次数: 0
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