Journal of the London Mathematical Society-Second Series最新文献

{"title":"Substitutions on compact alphabets","authors":"Neil Mañibo,&nbsp;Dan Rust,&nbsp;James J. Walton","doi":"10.1112/jlms.70123","DOIUrl":"https://doi.org/10.1112/jlms.70123","url":null,"abstract":"<p>We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised) subshifts. We then reframe questions from ergodic theory in terms of spectral properties of a corresponding substitution operator. This requires an extension of standard Perron–Frobenius theory to the setting of Banach lattices. As an application, we identify computable criteria that guarantee quasi-compactness of the substitution operator. This allows unique ergodicity to be verified for several classes of examples. For instance, it follows that every primitive and constant length substitution on an alphabet with an isolated point is uniquely ergodic, a result which fails when there are no isolated points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70123","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Carlson-type zero-density theorem for the Beurling \u0000 \u0000 ζ\u0000 $zeta$\u0000 function","authors":"Szilárd Gy. Révész","doi":"10.1112/jlms.70110","DOIUrl":"https://doi.org/10.1112/jlms.70110","url":null,"abstract":"<p>In a previous paper, we proved a Carlson-type density theorem for zeroes in the critical strip for the Beurling zeta functions satisfying Axiom A of Knopfmacher. There we needed to invoke two additional conditions: the integrality of the norm (Condition B) and an “average Ramanujan condition” for the arithmetical function counting the number of different Beurling integers of the same norm <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$min {mathbb {N}}$</annotation>\u0000 </semantics></math> (Condition G).</p><p>Here, we implement a new approach of Pintz using the classic zero-detecting sums coupled with Halász' method, but otherwise arguing in an elementary way avoiding, for example, large sieve-type inequalities or mean value estimates for Dirichlet polynomials. In this way, we give a new proof of a Carlson-type density estimate—with explicit constants—avoiding any use of the two additional conditions needed earlier.</p><p>Therefore, it is seen that the validity of a Carlson-type density estimate does not depend on any extra assumption—neither on the functional equation present for the Selberg class, nor on growth estimates of coefficients say of “average Ramanujan-type”—but is a general property presenting itself whenever the analytic continuation is guaranteed by Axiom A.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70110","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Set-theoretically perfect ideals and residual intersections","authors":"S. Hamid Hassanzadeh","doi":"10.1112/jlms.70108","DOIUrl":"https://doi.org/10.1112/jlms.70108","url":null,"abstract":"<p>This paper studies algebraic residual intersections in rings with Serre's condition <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mi>s</mi>\u0000 </msub>\u0000 <annotation>$ S_{s}$</annotation>\u0000 </semantics></math>. It demonstrates that a wide class of residual intersections is set theoretically perfect. This fact leads to determining a uniform upper bound for the multiplicity of residual intersections. In positive characteristic, it follows that residual intersections are cohomologically complete intersection, and hence, their variety is connected in codimension 1.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sparse systems with high local multiplicity","authors":"Frédéric Bihan,&nbsp;Alicia Dickenstein,&nbsp;Jens Forsgård","doi":"10.1112/jlms.70106","DOIUrl":"https://doi.org/10.1112/jlms.70106","url":null,"abstract":"&lt;p&gt;Consider a sparse system of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Laurent polynomials in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; variables with complex coefficients and support in a finite lattice set &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The maximal number of isolated roots of the system in the torus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$(mathbb {C}^*)^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is known to be the normalized volume of the convex hull of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (the BKK bound). We explore the following question: if the cardinality of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; equals &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$n+m+1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, what is the maximum local intersection multiplicity at one point in the torus in terms of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;annotation&gt;$m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;? This study was initiated by Gabrielov [13] in the multivariate case. We give an upper bound that is always sharp when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$m=1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and, under a technical hypothesis, it is considerably smaller than the previous upper bound for any dimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and codimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;annotation&gt;$m$&lt;/annotation","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponentials rarely maximize Fourier extension inequalities for cones","authors":"Giuseppe Negro,&nbsp;Diogo Oliveira e Silva,&nbsp;Betsy Stovall,&nbsp;James Tautges","doi":"10.1112/jlms.70112","DOIUrl":"https://doi.org/10.1112/jlms.70112","url":null,"abstract":"&lt;p&gt;We prove the existence of maximizers and the precompactness of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-normalized maximizing sequences modulo symmetries for all valid scale-invariant Fourier extension inequalities on the cone in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^{1+d}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In the range for which such inequalities are conjectural, our result is conditional on the boundedness of the extension operator. Global maximizers for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Fourier extension inequality on the cone in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^{1+d}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; have been characterized in the lowest dimensional cases &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$din lbrace 2,3rbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We further prove that these functions are critical points for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Fourier extension inequality if and only if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p = 2$&lt;/annotation&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70112","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Averaging multipliers on locally compact quantum groups","authors":"Matthew Daws,&nbsp;Jacek Krajczok,&nbsp;Christian Voigt","doi":"10.1112/jlms.70104","DOIUrl":"https://doi.org/10.1112/jlms.70104","url":null,"abstract":"<p>We study an averaging procedure for completely bounded multipliers on a locally compact quantum group with respect to a compact quantum subgroup. As a consequence we show that central approximation properties of discrete quantum groups are equivalent to the corresponding approximation properties of their Drinfeld doubles. This is complemented by a discussion of the averaging of Fourier algebra elements. We compare the biinvariant Fourier algebra of the Drinfeld double of a discrete quantum group with the central Fourier algebra. In the unimodular case these are naturally identified, but we show by exhibiting a family of counter-examples that they differ in general.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70104","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"All two-dimensional expanding Ricci solitons","authors":"Luke T. Peachey,&nbsp;Peter M. Topping","doi":"10.1112/jlms.70072","DOIUrl":"https://doi.org/10.1112/jlms.70072","url":null,"abstract":"<p>The second author and H. Yin [<i>Ars Inveniendi Analytica</i>. DOI 10.15781/4x5c-9q97] have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a non-atomic Radon measure as a volume measure. This led to the discovery of a large array of new expanding Ricci solitons. In this paper, we use the recent uniqueness theory in this context, also developed by the second author and H. Yin [<i>Proc. Lond. Math. Soc</i>. <b>128</b>:e12600 (2024)], to give a complete classification of all expanding Ricci solitons on surfaces. Along the way, we prove a converse to the existence theory that is not constrained to solitons: Every complete Ricci flow on a surface over a time interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>ε</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,varepsilon)$</annotation>\u0000 </semantics></math> admits a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>↓</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$tdownarrow 0$</annotation>\u0000 </semantics></math> limit within the class of admissible initial data. This makes surfaces the first non-trivial setting for Ricci flow in which a bijection can be given between the entire set of complete Ricci flows over maximal time intervals <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,T)$</annotation>\u0000 </semantics></math>, and a class of initial data that induce them.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70072","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparing Kähler cone and symplectic cone of one-point blowup of Enriques surface","authors":"Shengzhen Ning","doi":"10.1112/jlms.70117","DOIUrl":"https://doi.org/10.1112/jlms.70117","url":null,"abstract":"<p>We follow the study by Cascini–Panov on symplectic generic complex structures on Kähler surfaces with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$p_g=0$</annotation>\u0000 </semantics></math>, a question proposed by Li, by demonstrating that the one-point blowup of an Enriques surface admits non-Kähler symplectic forms. This phenomenon relies on the abundance of elliptic fibrations on Enriques surfaces, characterized by various invariants from the algebraic geometry. We also provide a quantitative comparison of these invariants to further give a detailed examination of the distinction between Kähler cone and symplectic cone.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ground states of a non-local variational problem and Thomas–Fermi limit for the Choquard equation","authors":"Damiano Greco,&nbsp;Yanghong Huang,&nbsp;Zeng Liu,&nbsp;Vitaly Moroz","doi":"10.1112/jlms.70115","DOIUrl":"https://doi.org/10.1112/jlms.70115","url":null,"abstract":"<p>We study non-negative optimisers of a Gagliardo–Nirenberg-type inequality\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70115","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adhesion and volume filling in one-dimensional population dynamics under no-flux boundary condition","authors":"Hyung Jun Choi,&nbsp;Seonghak Kim,&nbsp;Youngwoo Koh","doi":"10.1112/jlms.70113","DOIUrl":"https://doi.org/10.1112/jlms.70113","url":null,"abstract":"<p>We study the (generalized) one-dimensional population model developed by Anguige and Schmeiser [J. Math. Biol. 58 (3) (2009), 395–427], which reflects cell–cell adhesion and volume filling under no-flux boundary condition. In this generalized model, depending on the adhesion and volume filling parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$alpha,beta in [0,1]$</annotation>\u0000 </semantics></math>, the resulting equation is classified into six types. Among these, we focus on the type exhibiting strong effects of both adhesion and volume filling, which results in a class of advection–diffusion equations of the forward–backward–forward type. For five distinct cases of initial maximum, minimum, and average population densities, we derive the corresponding patterns for the global behavior of weak solutions to the initial and no-flux boundary value problem. Due to the presence of a negative diffusion regime, we indeed prove that the problem is ill-posed and admits infinitely many global-in-time weak solutions, with the exception of one specific case of the initial datum. This nonuniqueness is inherent in the method of convex integration that we use to solve the Dirichlet problem of a partial differential inclusion arising from the ill-posed problem.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}