{"title":"Exponential convergence to equilibrium of solutions of the Kac equation and homogeneous Boltzmann equation for Maxwellian without angular cut-off","authors":"Fei Meng, Xiao-Ping Yang","doi":"10.3233/ASY-171407","DOIUrl":"https://doi.org/10.3233/ASY-171407","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"12 1","pages":"251-271"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82799890","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}
In this paper, we study the asymptotic behavior of nonlinear Klein-Gordon equations in the non-relativistic limit regime. By employing the techniques in geometric optics, we show that the Klein-Gordon equation can be approximated by nonlinear Schrödinger equations. In particular, we show error estimates which are of the same order as the initial error. Our result gives a mathematical verification for some numerical results obtained in [1, 2], and offers a rigorous justification for a technical assumption in the numerical studies [1].
{"title":"Higher order asymptotic analysis of the Klein-Gordon equation in the non-relativistic limit regime","authors":"Yong Lu, Zhifei Zhang","doi":"10.3233/ASY-171414","DOIUrl":"https://doi.org/10.3233/ASY-171414","url":null,"abstract":"In this paper, we study the asymptotic behavior of nonlinear Klein-Gordon equations in the non-relativistic limit regime. By employing the techniques in geometric optics, we show that the Klein-Gordon equation can be approximated by nonlinear Schrödinger equations. In particular, we show error estimates which are of the same order as the initial error. Our result gives a mathematical verification for some numerical results obtained in [1, 2], and offers a rigorous justification for a technical assumption in the numerical studies [1].","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"197 1","pages":"157-175"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72919310","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":"Development of congestion in compressible flow with singular pressure","authors":"D. Bresch, M. Renardy","doi":"10.3233/ASY-171421","DOIUrl":"https://doi.org/10.3233/ASY-171421","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"42 1","pages":"95-101"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76374348","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":"High frequency approximation of solutions to Klein-Gordon equation in Orlicz framework","authors":"I. B. Ayed","doi":"10.3233/ASY-161398","DOIUrl":"https://doi.org/10.3233/ASY-161398","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"28 1","pages":"181-206"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79688414","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":"Asymptotic behavior of a model for order-disorder and phase separation","authors":"A. Miranville, Wafa Saoud, Raafat Talhouk","doi":"10.3233/ASY-171419","DOIUrl":"https://doi.org/10.3233/ASY-171419","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"13 1","pages":"57-76"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84648663","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":"Mathematical justification of the obstacle problem for a piezoelectric shallow shell","authors":"G. Yan, B. Miara","doi":"10.3233/ASY-171411","DOIUrl":"https://doi.org/10.3233/ASY-171411","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"39 1","pages":"71-97"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73917335","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}
In this paper we discuss a damage model that is based on microstructure evolution. In the context of evolutionary Γ-convergence we derive a corresponding effective macroscopic model. In this model, the damage state of a given material point is related to a unit cell problem incorporating a specific microscopic defect. The size and shape of this underlying microscopic defect is determined by the evolution. According to the small intrinsic length scale inherent to the original models a numerical simulation of damage progression in a device of realistic size is hopeless. Due to the scale separation in the effective model, its numerical treatment seems promising.
{"title":"A phase-field damage model based on evolving microstructure","authors":"H. Hanke, D. Knees","doi":"10.3233/ASY-161396","DOIUrl":"https://doi.org/10.3233/ASY-161396","url":null,"abstract":"In this paper we discuss a damage model that is based on microstructure evolution. In the context of evolutionary Γ-convergence we derive a corresponding effective macroscopic model. In this model, the damage state of a given material point is related to a unit cell problem incorporating a specific microscopic defect. The size and shape of this underlying microscopic defect is determined by the evolution. According to the small intrinsic length scale inherent to the original models a numerical simulation of damage progression in a device of realistic size is hopeless. Due to the scale separation in the effective model, its numerical treatment seems promising.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"23 1","pages":"149-180"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83930106","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":"Existence and stability of the steady state solution of a thin film on an inclined periodic solid substrate under gravity","authors":"Ahmad Alhasanat, Chunhua Ou","doi":"10.3233/ASY-171431","DOIUrl":"https://doi.org/10.3233/ASY-171431","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"17 1","pages":"191-207"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88826781","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":"Spectral analysis of a non-selfadjoint operator generated by an energy harvesting model and application to an exact controllability problem","authors":"M. Shubov","doi":"10.3233/ASY-171413","DOIUrl":"https://doi.org/10.3233/ASY-171413","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"27 1","pages":"119-156"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89402401","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":"The Cahn-Hilliard equation as limit of a conserved phase-field system","authors":"A. Bonfoh, C. Enyi","doi":"10.3233/ASY-161395","DOIUrl":"https://doi.org/10.3233/ASY-161395","url":null,"abstract":"","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"26 1","pages":"97-148"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89601641","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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