Pub Date : 2023-01-01DOI: 10.4310/maa.2023.v30.n1.a1
Natsumi Yoshida
{"title":"Global asymptotic stability of the rarefaction waves to the Cauchy problem for the generalized Rosenau–Korteweg–de Vries–Burgers equation","authors":"Natsumi Yoshida","doi":"10.4310/maa.2023.v30.n1.a1","DOIUrl":"https://doi.org/10.4310/maa.2023.v30.n1.a1","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70490090","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}
Pub Date : 2023-01-01DOI: 10.4310/maa.2023.v30.n1.a2
De-Jun Feng, H. Ruan, Ying Xiong
{"title":"On separation properties for iterated function systems of similitudes","authors":"De-Jun Feng, H. Ruan, Ying Xiong","doi":"10.4310/maa.2023.v30.n1.a2","DOIUrl":"https://doi.org/10.4310/maa.2023.v30.n1.a2","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70490103","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n1.a4
Dongcheng Yang, Hongjun Yu
In this paper, we construct the global solutions near a local Maxwellian for the onedimensional two-species Vlasov-Poisson-Boltzmann system with soft potentials. The macroscopic components of this local Maxwellian are the approximate rarefaction wave solutions to the associated one-dimensional compressible Euler system. Then we prove the stability of the rarefaction waves for the two-species Vlasov-Poisson-Boltzmann system in the weighted function space. Moreover, some time decay rates of the disparity between two species and the electric field are obtained.
{"title":"Stability of rarefaction waves for the two-species Vlasov–Poisson–Boltzmann system with soft potentials","authors":"Dongcheng Yang, Hongjun Yu","doi":"10.4310/maa.2022.v29.n1.a4","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n1.a4","url":null,"abstract":"In this paper, we construct the global solutions near a local Maxwellian for the onedimensional two-species Vlasov-Poisson-Boltzmann system with soft potentials. The macroscopic components of this local Maxwellian are the approximate rarefaction wave solutions to the associated one-dimensional compressible Euler system. Then we prove the stability of the rarefaction waves for the two-species Vlasov-Poisson-Boltzmann system in the weighted function space. Moreover, some time decay rates of the disparity between two species and the electric field are obtained.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489848","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n1.a5
Chenxi Zheng, Shaoqiang Tang
. Although several short-time simulations have been reported nicely reproducing rogue wave solutions in the nonlinear Schr¨odinger equation, rogue wave solutions are linearly unstable as shown by theoretical studies. In the present work, we perform long-time simulations for two kinds of rogue wave solutions, namely, the Akhmediev breather and Peregrine soliton. Numerical evidences demonstrate that spurious oscillations that emerge in the central domain in both simulations arise from round-off error and evolve under the mechanism of modulational instability. For the periodic approximation of the Peregrine soliton, the modulational instability also gives rise to additional oscillations on the boundary. We obtain a fitting formula to forecast the time when the boundary oscillations occur. Our simulation results show that a clean and faithful long-time reproduction of rogue wave solutions would be difficult because of the modulational instability.
{"title":"Long-time simulations of rogue wave solutions in the nonlinear Schrödinger equation","authors":"Chenxi Zheng, Shaoqiang Tang","doi":"10.4310/maa.2022.v29.n1.a5","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n1.a5","url":null,"abstract":". Although several short-time simulations have been reported nicely reproducing rogue wave solutions in the nonlinear Schr¨odinger equation, rogue wave solutions are linearly unstable as shown by theoretical studies. In the present work, we perform long-time simulations for two kinds of rogue wave solutions, namely, the Akhmediev breather and Peregrine soliton. Numerical evidences demonstrate that spurious oscillations that emerge in the central domain in both simulations arise from round-off error and evolve under the mechanism of modulational instability. For the periodic approximation of the Peregrine soliton, the modulational instability also gives rise to additional oscillations on the boundary. We obtain a fitting formula to forecast the time when the boundary oscillations occur. Our simulation results show that a clean and faithful long-time reproduction of rogue wave solutions would be difficult because of the modulational instability.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489865","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n2.a2
V. Menegatto, C. Oliveira
{"title":"An extension of Aitken’s integral for Gaussians and positive definiteness","authors":"V. Menegatto, C. Oliveira","doi":"10.4310/maa.2022.v29.n2.a2","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n2.a2","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"164 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489934","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n2.a4
N. Jiang
{"title":"On the convergence of a second-order nonlinear SSP Runge–Kutta method for convex scalar conservation laws","authors":"N. Jiang","doi":"10.4310/maa.2022.v29.n2.a4","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n2.a4","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489995","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n1.a2
Shasha Wang, Wen-Qing Xu, Jitao Liu
{"title":"Global well-posedness and large time behavior to 2D Boussinesq equations for MHD convection","authors":"Shasha Wang, Wen-Qing Xu, Jitao Liu","doi":"10.4310/maa.2022.v29.n1.a2","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n1.a2","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489518","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n3.a1
C. Nonato, C. Raposo, W. D. Bastos
{"title":"A transmission problem for waves under time-varying delay and time-varying weights","authors":"C. Nonato, C. Raposo, W. D. Bastos","doi":"10.4310/maa.2022.v29.n3.a1","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n3.a1","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70490009","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n3.a2
B. Carbonaro, Marco Menale
{"title":"The inverse problem for the reconstruction of the weight functions in a socio-economic system modelled by the discrete thermostatted kinetic framework","authors":"B. Carbonaro, Marco Menale","doi":"10.4310/maa.2022.v29.n3.a2","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n3.a2","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70490041","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}
Pub Date : 2022-01-01DOI: 10.4310/maa.2022.v29.n2.a1
Bilal Al Taki
{"title":"A note on functional inequalities and entropies estimates for some higher-order nonlinear PDEs","authors":"Bilal Al Taki","doi":"10.4310/maa.2022.v29.n2.a1","DOIUrl":"https://doi.org/10.4310/maa.2022.v29.n2.a1","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70489918","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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