O. A. Hafsa, Jean-Philippe Mandallena, G. Michaille
We establish a convergence theorem for a class of nonlinear reaction-diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of functionals of the calculus of variations equipped with the Mosco-convergence. The reaction term, which is not globally Lipschitz with respect to the state variable, gives rise to bounded solutions, and cover a wide variety of models. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.
{"title":"Stability of a class of nonlinear reaction-diffusion equations and stochastic homogenization","authors":"O. A. Hafsa, Jean-Philippe Mandallena, G. Michaille","doi":"10.3233/asy-191531","DOIUrl":"https://doi.org/10.3233/asy-191531","url":null,"abstract":"We establish a convergence theorem for a class of nonlinear reaction-diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of functionals of the calculus of variations equipped with the Mosco-convergence. The reaction term, which is not globally Lipschitz with respect to the state variable, gives rise to bounded solutions, and cover a wide variety of models. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"31 4","pages":"169-221"},"PeriodicalIF":0.0,"publicationDate":"2019-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91504132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Bazarra, José R. Fernández, M. C. Leseduarte, A. Magaña, R. Quintanilla
In this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained.
{"title":"On the uniqueness and analyticity in viscoelasticity with double porosity","authors":"N. Bazarra, José R. Fernández, M. C. Leseduarte, A. Magaña, R. Quintanilla","doi":"10.3233/ASY-181500","DOIUrl":"https://doi.org/10.3233/ASY-181500","url":null,"abstract":"In this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"17 1","pages":"151-164"},"PeriodicalIF":0.0,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80467061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter (cid:2) . We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For (cid:2) small, we prove that the effective conductivity can be represented as a convergent power series in (cid:2) and we determine the coefficients in terms of the solutions of explicit systems of integral equations.
{"title":"Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface","authors":"M. D. Riva, P. Musolino, R. Pukhtaievych","doi":"10.3233/ASY-181495","DOIUrl":"https://doi.org/10.3233/ASY-181495","url":null,"abstract":". We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter (cid:2) . We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For (cid:2) small, we prove that the effective conductivity can be represented as a convergent power series in (cid:2) and we determine the coefficients in terms of the solutions of explicit systems of integral equations.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"101 1","pages":"217-250"},"PeriodicalIF":0.0,"publicationDate":"2019-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80605189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.
{"title":"Umov-Poynting-Mandelstam radiation conditions in periodic composite piezoelectric waveguides","authors":"G. Leugering, S. Nazarov, J. Taskinen","doi":"10.3233/ASY-181487","DOIUrl":"https://doi.org/10.3233/ASY-181487","url":null,"abstract":"We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":" 10","pages":"69-111"},"PeriodicalIF":0.0,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91413088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonexistence results for systems of parabolic differential inequalities in 2D exterior domains","authors":"M. Jleli, B. Samet","doi":"10.3233/ASY-181506","DOIUrl":"https://doi.org/10.3233/ASY-181506","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"124 1","pages":"29-49"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77475440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Diffusion process in a perforated domain around a vanishing suspension","authors":"Selwa Chennouf, F. Bentalha","doi":"10.3233/asy-191529","DOIUrl":"https://doi.org/10.3233/asy-191529","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"87 1","pages":"127-145"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81227338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On asymptotic forms of solutions to the Riccati equation","authors":"V. S. Samovol","doi":"10.3233/asy-191534","DOIUrl":"https://doi.org/10.3233/asy-191534","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"88 1","pages":"223-239"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79727181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lu Li, Xinguang Yang, Xuezhi Li, Xingjie Yan, Yongjin Lu
{"title":"Dynamics and stability of the 3D Brinkman-Forchheimer equation with variable delay (I)","authors":"Lu Li, Xinguang Yang, Xuezhi Li, Xingjie Yan, Yongjin Lu","doi":"10.3233/ASY-181512","DOIUrl":"https://doi.org/10.3233/ASY-181512","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"6 1","pages":"167-194"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81169709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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