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Maximal Lp-regularity of an abstract evolution equation: Application to closed-loop feedback problems, with boundary controls and boundary sensors
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-21 DOI: 10.1016/j.nonrwa.2024.104295
Irena Lasiecka , Buddhika Priyasad , Roberto Triggiani
{"title":"Maximal Lp-regularity of an abstract evolution equation: Application to closed-loop feedback problems, with boundary controls and boundary sensors","authors":"Irena Lasiecka ,&nbsp;Buddhika Priyasad ,&nbsp;Roberto Triggiani","doi":"10.1016/j.nonrwa.2024.104295","DOIUrl":"10.1016/j.nonrwa.2024.104295","url":null,"abstract":"<div><div>We present an abstract maximal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-regularity result up to <span><math><mrow><mi>T</mi><mo>=</mo><mi>∞</mi></mrow></math></span> on a Banach space, that is tuned to capture (linear) PDEs of parabolic type, defined on a bounded domain and subject to finite dimensional, boundary controls and boundary sensors, in feedback form. It improves Lasiecka et al. (2021), which covered boundary controls and interior sensors. The present proof must necessarily be completely different from the one in Lasiecka et al. (2021). In applications (Section 3), the case <span><math><mrow><mi>T</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span> requires no further assumptions on the boundary control/sensor vectors. Instead, the case <span><math><mrow><mi>T</mi><mo>=</mo><mi>∞</mi></mrow></math></span> requires, of course, the property of uniform stabilization for suitable boundary control/sensor vectors, which is geometrically sensitive.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104295"},"PeriodicalIF":1.8,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Low Mach number limit for the compressible Euler-Navier-Stokes two-phase flow model in R3
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-16 DOI: 10.1016/j.nonrwa.2024.104267
Hakho Hong, Kwang-Hyon Jong
{"title":"Low Mach number limit for the compressible Euler-Navier-Stokes two-phase flow model in R3","authors":"Hakho Hong,&nbsp;Kwang-Hyon Jong","doi":"10.1016/j.nonrwa.2024.104267","DOIUrl":"10.1016/j.nonrwa.2024.104267","url":null,"abstract":"<div><div>This paper is concerned with the two-phase flow model consisting of the compressible isothermal Euler equations coupled with the compressible isentropic Navier-Stokes equations through a drag forcing term.For the 3-D Cauchy problem,we rigorously justify the low Mach number limit, which means that the solutions converge to that of a two-phase flow model coupled with the compressible Euler equations and the incom pressible Navier-Stokes equations locally and globally in time as Mach number goes to zero.</div><div>MSC 2020:35Q30,35B35,35L6576D3374J40</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104267"},"PeriodicalIF":1.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179283","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}
引用次数: 0
Improved decay results for micropolar flows with nonlinear damping
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-10 DOI: 10.1016/j.nonrwa.2024.104275
Cilon F. Perusato , Franco D. Vega
{"title":"Improved decay results for micropolar flows with nonlinear damping","authors":"Cilon F. Perusato ,&nbsp;Franco D. Vega","doi":"10.1016/j.nonrwa.2024.104275","DOIUrl":"10.1016/j.nonrwa.2024.104275","url":null,"abstract":"<div><div>We examine the long-time behavior of solutions (and their derivatives) to the micropolar equations with nonlinear velocity damping. Additionally, we get a speed-up gain of <span><math><msup><mrow><mi>t</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> for the angular velocity, consistent with established findings for classic micropolar flows lacking nonlinear damping. Consequently, we also obtain a sharper result regarding the asymptotic stability of the micro-rotational velocity <span><math><mrow><mi>w</mi><mrow><mo>(</mo><mi>⋅</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>. Related results of independent interest are also included.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104275"},"PeriodicalIF":1.8,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178793","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}
引用次数: 0
Well-posedness analysis of the Cahn–Hilliard–Biot model
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-09 DOI: 10.1016/j.nonrwa.2024.104271
Cedric Riethmüller , Erlend Storvik , Jakub Wiktor Both , Florin Adrian Radu
{"title":"Well-posedness analysis of the Cahn–Hilliard–Biot model","authors":"Cedric Riethmüller ,&nbsp;Erlend Storvik ,&nbsp;Jakub Wiktor Both ,&nbsp;Florin Adrian Radu","doi":"10.1016/j.nonrwa.2024.104271","DOIUrl":"10.1016/j.nonrwa.2024.104271","url":null,"abstract":"<div><div>We investigate the well-posedness of the recently proposed Cahn–Hilliard–Biot model. The model is a three-way coupled PDE of elliptic–parabolic nature, with several nonlinearities and the fourth order term known to the Cahn–Hilliard system. We show existence of weak solutions to the variational form of the equations and uniqueness under certain conditions of the material parameters and secondary consolidation, adding regularizing effects. Existence is shown by discretizing in space and applying ODE-theory (the Peano–Cauchy theorem) to prove existence of the discrete system, followed by compactness arguments to retain solutions of the continuous system. In addition, the continuous dependence of solutions on the data is established, in particular implying uniqueness. Both results build strongly on the inherent gradient flow structure of the model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104271"},"PeriodicalIF":1.8,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topological and control theoretic properties of Hamilton–Jacobi equations via Lax-Oleinik commutators
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-07 DOI: 10.1016/j.nonrwa.2024.104282
Piermarco Cannarsa , Wei Cheng , Jiahui Hong
{"title":"Topological and control theoretic properties of Hamilton–Jacobi equations via Lax-Oleinik commutators","authors":"Piermarco Cannarsa ,&nbsp;Wei Cheng ,&nbsp;Jiahui Hong","doi":"10.1016/j.nonrwa.2024.104282","DOIUrl":"10.1016/j.nonrwa.2024.104282","url":null,"abstract":"<div><div>In the context of weak KAM theory, we discuss the commutators <span><math><msub><mrow><mrow><mo>{</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>∘</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>}</mo></mrow></mrow><mrow><mi>t</mi><mo>⩾</mo><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mrow><mo>{</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>∘</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>}</mo></mrow></mrow><mrow><mi>t</mi><mo>⩾</mo><mn>0</mn></mrow></msub></math></span> of Lax-Oleinik operators. We characterize the relation <span><math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>∘</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>=</mo><mi>I</mi><mi>d</mi></mrow></math></span> for both small time and arbitrary time <span><math><mi>t</mi></math></span>. We show this relation characterizes controllability for evolutionary Hamilton–Jacobi equation. Based on our previous work on the cut locus of viscosity solution, we refine our analysis of the cut time function <span><math><mi>τ</mi></math></span> in terms of commutators <span><math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>∘</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>∘</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow></math></span> and clarify the structure of the super/sub-level set of the cut time function <span><math><mi>τ</mi></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104282"},"PeriodicalIF":1.8,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178843","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}
引用次数: 0
Strong and weak solutions of history-dependent constrained evolutionary variational–hemivariational inequalities and application
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-06 DOI: 10.1016/j.nonrwa.2024.104273
Stanisław Migórski , Yunru Bai , Sylwia Dudek
{"title":"Strong and weak solutions of history-dependent constrained evolutionary variational–hemivariational inequalities and application","authors":"Stanisław Migórski ,&nbsp;Yunru Bai ,&nbsp;Sylwia Dudek","doi":"10.1016/j.nonrwa.2024.104273","DOIUrl":"10.1016/j.nonrwa.2024.104273","url":null,"abstract":"<div><div>In this paper we study the well-posedness of evolutionary variational–hemivariational inequalities involving constraint and history-dependent operators. The strong and weak formulations of such inequalities are analysed. First, the existence and uniqueness of solutions to both formulations are proved, and results on solution dependence on functional parameters are delivered. Then, exploiting a fixed point argument, the well-posedness is established for a general form of history-dependent variational–hemivariational inequalities with constraints. As an illustrative example, we apply the theory to a dynamic frictional contact problem in viscoelasticity in which the contact is described by a frictionless Signorini-type unilateral boundary condition with a nonmonotone Clarke’s relation and the friction is modelled by a generalization of the evolutionary version of Coulomb’s law of dry friction with the friction bound depending on the normal and tangential components of the displacement.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104273"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178799","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}
引用次数: 0
Global well-posedness for the compressible Euler–Korteweg equations with damping in L2-Lp critical Besov space and relaxation limit
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-06 DOI: 10.1016/j.nonrwa.2024.104274
Jianzhong Zhang , Hongmei Cao
{"title":"Global well-posedness for the compressible Euler–Korteweg equations with damping in L2-Lp critical Besov space and relaxation limit","authors":"Jianzhong Zhang ,&nbsp;Hongmei Cao","doi":"10.1016/j.nonrwa.2024.104274","DOIUrl":"10.1016/j.nonrwa.2024.104274","url":null,"abstract":"<div><div>In this paper, we investigate the Cauchy problem of compressible Euler–Korteweg equations with damping. The global well-posedness is established in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-<span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> critical Besov spaces. In our results, the existence theorem provides us with bounds that are <em>independent</em> of the relaxation parameter <span><math><mi>ɛ</mi></math></span> and capillary coefficient <span><math><mi>k</mi></math></span>. As a consequence, we rigorously justify the relaxation limit and study the effect of the Korteweg-type dispersion on the relaxation limit. Specially, when <span><math><mrow><mi>k</mi><mo>≡</mo><mn>0</mn></mrow></math></span>, our theorems reduce to the results in Crin-Barat and Danchin (2022) [28,29] on the Euler system with damping, and the smallness assumption for low-frequency initial data of velocity is weaker in some way.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104274"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179285","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}
引用次数: 0
A note on collectively coincidence theory for lower semicontinuous maps
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-06 DOI: 10.1016/j.nonrwa.2024.104272
Donal O’Regan
{"title":"A note on collectively coincidence theory for lower semicontinuous maps","authors":"Donal O’Regan","doi":"10.1016/j.nonrwa.2024.104272","DOIUrl":"10.1016/j.nonrwa.2024.104272","url":null,"abstract":"<div><div>In this paper we present collectively fixed point theory for lower semicontinuous maps. In addition we present coincidence results between <span><math><mrow><mi>K</mi><mi>K</mi><mi>M</mi></mrow></math></span> type maps and lower semicontinuous maps. Our arguments are based on the Schauder-Tychonoff fixed point theorem and a fixed point result based on <span><math><mrow><mi>K</mi><mi>K</mi><mi>M</mi></mrow></math></span> self maps on an admissible convex set in a Hausdorff topological vector space. As an application we present a new (Nash) equilibrium result for economies.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104272"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179286","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}
引用次数: 0
Traveling waves in reaction–diffusion–convection equations with combustion nonlinearity
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-06 DOI: 10.1016/j.nonrwa.2024.104283
Pavel Drábek , Michaela Zahradníková
{"title":"Traveling waves in reaction–diffusion–convection equations with combustion nonlinearity","authors":"Pavel Drábek ,&nbsp;Michaela Zahradníková","doi":"10.1016/j.nonrwa.2024.104283","DOIUrl":"10.1016/j.nonrwa.2024.104283","url":null,"abstract":"<div><div>This paper concerns the existence and properties of traveling wave solutions to reaction–diffusion–convection equations on the real line. We consider a general diffusion term involving the <span><math><mi>p</mi></math></span>-Laplacian and combustion-type reaction term. We extend and generalize results established for <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span> to the case of singular and degenerate diffusion. Our approach allows for non-Lipschitz reaction as well. We also discuss the shape of the traveling wave profile near equilibria, assuming power-type behavior of the reaction and diffusion terms.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104283"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178798","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}
引用次数: 0
Anisotropic flows of Forchheimer-type in porous media and their steady states
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2024-12-04 DOI: 10.1016/j.nonrwa.2024.104269
Luan Hoang , Thinh Kieu
{"title":"Anisotropic flows of Forchheimer-type in porous media and their steady states","authors":"Luan Hoang ,&nbsp;Thinh Kieu","doi":"10.1016/j.nonrwa.2024.104269","DOIUrl":"10.1016/j.nonrwa.2024.104269","url":null,"abstract":"<div><div>We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically satisfied in this case. Therefore, various sufficient conditions for them are derived and applied to the experimental data. In the second half of the paper, we prove the existence and uniqueness of the steady state flows subject to a nonhomogeneous Dirichlet boundary condition. It is also established that these steady states, in appropriate functional spaces, have local Hölder continuous dependence on the forcing function and the boundary data.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104269"},"PeriodicalIF":1.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179287","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}
引用次数: 0
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