{"title":"On theoretical result of a controlled $ p(x) $-reaction diffusion equation for Poisson noise reduction","authors":"M. Nachaoui, A. Laghrib, A. El Hakoume","doi":"10.3934/eect.2023045","DOIUrl":"https://doi.org/10.3934/eect.2023045","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"12 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74103869","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}
A. Bensalem, Abdelkrim Salim, M. Benchohra, J. Nieto
{"title":"Controllability results for second-order integro-differential equations with state-dependent delay","authors":"A. Bensalem, Abdelkrim Salim, M. Benchohra, J. Nieto","doi":"10.3934/eect.2023026","DOIUrl":"https://doi.org/10.3934/eect.2023026","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"248 ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72434316","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":"Null Boundary Controllability for some Biological and Chemical Diffusion Problems","authors":"M. Ismailov, Isil Oner","doi":"10.3934/eect.2023012","DOIUrl":"https://doi.org/10.3934/eect.2023012","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87109423","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}
In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.
研究了一类具有对数非线性的伪抛物型$ p $-Kirchhoff方程的初边值问题。通过证明该问题半流下不稳定集的不变性，采用Levine的凹性论证，建立了该问题的一般有限时间爆破判据，特别表明对于某些初始数据，该问题在任意高的初始能级上允许有限时间爆破解。此外，爆破解决方案的寿命是从上面估计的。
{"title":"Blow-up for a pseudo-parabolic $ p $-Kirchhoff equation with logarithmic nonlinearity","authors":"Hui Yang","doi":"10.3934/eect.2023053","DOIUrl":"https://doi.org/10.3934/eect.2023053","url":null,"abstract":"In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319484","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}
This paper studies a non-autonomous incompressible non-Newtonian fluid with delay in a 2D unbounded domain. The existence of pullback $ mathcal{D} $ attractor with $ mathbb{H}^2 $ regularity is obtained and its relationship with the pullback $ mathcal{D} $ attractor with $ mathbb{L}^2 $ regularity obtained in [25] is also shown. This fact exhibits the pullback smoothing effect of the fluid with delays.
{"title":"Existence and regularity of pullback attractors for a non-Newtonian fluid with delays in 2D unbounded domains","authors":"Guowei Liu, Hao Xu, Caidi Zhao","doi":"10.3934/eect.2023050","DOIUrl":"https://doi.org/10.3934/eect.2023050","url":null,"abstract":"This paper studies a non-autonomous incompressible non-Newtonian fluid with delay in a 2D unbounded domain. The existence of pullback $ mathcal{D} $ attractor with $ mathbb{H}^2 $ regularity is obtained and its relationship with the pullback $ mathcal{D} $ attractor with $ mathbb{L}^2 $ regularity obtained in [25] is also shown. This fact exhibits the pullback smoothing effect of the fluid with delays.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135555705","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":"Feedback control problems for a class of backward Riemann-Liouville fractional evolution hemivariational inequalities with dual operators","authors":"Jianguang Liu, F. Hu, Yi‐rong Jiang","doi":"10.3934/eect.2023043","DOIUrl":"https://doi.org/10.3934/eect.2023043","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"90 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82267518","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}
In this paper, we study the stability of an infinite star-shaped network of a linear viscous damped wave equation. We prove that, under some conditions, the whole system is asymptotically stable. Moreover we give a decay rate of the energy of the solution. Our technique is based on a frequency domain method.
{"title":"Stability of a damped wave equation on an infinite star-shaped network","authors":"Ahmed Bchatnia, Amina Boukhatem","doi":"10.3934/eect.2022024","DOIUrl":"https://doi.org/10.3934/eect.2022024","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we study the stability of an infinite star-shaped network of a linear viscous damped wave equation. We prove that, under some conditions, the whole system is asymptotically stable. Moreover we give a decay rate of the energy of the solution. Our technique is based on a frequency domain method.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135182954","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":"An effect of decay rates: Supercritical damping and a viscoelastic term","authors":"Fang Li, Xiaolei Li","doi":"10.3934/eect.2023038","DOIUrl":"https://doi.org/10.3934/eect.2023038","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"43 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83550188","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}
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