Journal of Evolution Equations最新文献

{"title":"Doubly nonlinear equations for the 1-Laplacian","authors":"J. M. Mazón, A. Molino, J. Toledo","doi":"10.1007/s00028-023-00917-8","DOIUrl":"https://doi.org/10.1007/s00028-023-00917-8","url":null,"abstract":"Abstract This paper is concerned with the Neumann problem for a class of doubly nonlinear equations for the 1-Laplacian, $$begin{aligned} frac{partial v}{partial t} - Delta _1 u ni 0 hbox { in } (0, infty ) times Omega , quad vin gamma (u), end{aligned}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>Δ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>∋</mml:mo> <mml:mn>0</mml:mn> <mml:mspace /> <mml:mtext>in</mml:mtext> <mml:mspace /> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:mi>Ω</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>v</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math> and initial data in $$L^1(Omega )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , where $$Omega $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Ω</mml:mi> </mml:math> is a bounded smooth domain in $${mathbb {R}}^N$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> </mml:math> and $$gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>γ</mml:mi> </mml:math> is a maximal monotone graph in $${mathbb {R}}times {mathbb {R}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>×</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> . We prove that, under certain assumptions on the graph $$gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>γ</mml:mi> </mml:math> , there is existence and uniqueness of solutions. Moreover, we proof that these solutions coincide with the ones of the Neumann problem for the total variational flow. We show that such assumptions are necessary.","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frequency theorem and inertial manifolds for neutral delay equations","authors":"Mikhail Anikushin","doi":"10.1007/s00028-023-00915-w","DOIUrl":"https://doi.org/10.1007/s00028-023-00915-w","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques","authors":"Ning-An Lai, Nico Michele Schiavone","doi":"10.1007/s00028-023-00918-7","DOIUrl":"https://doi.org/10.1007/s00028-023-00918-7","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ill-posedness of the Cauchy problem for the $$mu $$-Camassa–Holm-type equations","authors":"Kexin Yan, Hao Wang, Ying Fu","doi":"10.1007/s00028-023-00913-y","DOIUrl":"https://doi.org/10.1007/s00028-023-00913-y","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136342605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability for a composite of Timoshenko laminated beams","authors":"M. S. Alves, R. N. Monteiro","doi":"10.1007/s00028-023-00911-0","DOIUrl":"https://doi.org/10.1007/s00028-023-00911-0","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135535712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the admissibility of observation operators in the context of maximal regularity","authors":"O. El Mennaoui, S. Hadd, Y. Kharou","doi":"10.1007/s00028-023-00912-z","DOIUrl":"https://doi.org/10.1007/s00028-023-00912-z","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135397030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modified scattering for the fractional mKdV equation","authors":"N. Hayashi, P. Naumkin","doi":"10.1007/s00028-023-00910-1","DOIUrl":"https://doi.org/10.1007/s00028-023-00910-1","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75359371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted energy method for semilinear wave equations with time-dependent damping","authors":"M. Sobajima","doi":"10.1007/s00028-023-00908-9","DOIUrl":"https://doi.org/10.1007/s00028-023-00908-9","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74567847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the existence and Hölder regularity of solutions to some nonlinear Cauchy–Neumann problems","authors":"A. Audrito","doi":"10.1007/s00028-023-00899-7","DOIUrl":"https://doi.org/10.1007/s00028-023-00899-7","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82324536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation","authors":"N. Carreño, Cristóbal Loyola","doi":"10.1007/s00028-023-00907-w","DOIUrl":"https://doi.org/10.1007/s00028-023-00907-w","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72371708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}