Journal of Mathematical Analysis and Applications最新文献

{"title":"On the algebraic lower bound for the radius of spatial analyticity for the Zakharov-Kuznetsov and modified Zakharov-Kuznetsov equations","authors":"Mikaela Baldasso, Mahendra Panthee","doi":"10.1016/j.jmaa.2025.129802","DOIUrl":"10.1016/j.jmaa.2025.129802","url":null,"abstract":"<div><div>We consider the initial value problem (IVP) for the 2D generalized Zakharov-Kuznetsov (ZK) equation<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>μ</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> where <span><math><mi>Δ</mi><mo>=</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>, <span><math><mi>μ</mi><mo>=</mo><mo>±</mo><mn>1</mn></math></span>, <span><math><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> and the initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is real analytic in a complex strip in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and have radius of spatial analyticity <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. For both <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, considering a symmetrized version, we prove that there exists <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>0</mn></math></span> such that the radius of spatial analyticity of the solution remains the same in the time interval <span><math><mo>[</mo><mo>−</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>]</mo></math></span>. We also consider the evolution of the radius of spatial analyticity when the local solution extends globally in time. For the Zakharov-Kuznetsov equation (<span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span>), we prove that, in both focusing (<span><math><mi>μ</mi><mo>=</mo><mn>1</mn></math></span>) and defocusing (<span><math><mi>μ</mi><mo>=</mo><mo>−</mo><mn>1</mn></math></span>) cases, and for any <span><math><mi>T</mi><mo>></mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the radius of analyticity cannot decay faster than <span><math><mi>c</mi><msup><mrow><mi>T</mi></mrow><mrow><mo>−</mo><mo>(</mo>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129802"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471156","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":"Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds","authors":"Fabrice Baudoin ,&nbsp;Hongyi Chen ,&nbsp;Cheng Ouyang","doi":"10.1016/j.jmaa.2025.129805","DOIUrl":"10.1016/j.jmaa.2025.129805","url":null,"abstract":"<div><div>We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space indexed by a regularity parameter <em>α</em>, which we use to explore regularity requirements for well-posedness. Then, we show that conditions on the heat kernel imply an exponential in time upper bound for the moments of the solution, and a lower bound for sectional curvature implies a corresponding lower bound. These results hold if the noise is strong enough, where the needed strength of the noise is affected by sectional curvature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129805"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517361","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":"Local and global bifurcation analysis of density-suppressed motility model","authors":"Di Liu ,&nbsp;Junping Shi ,&nbsp;Weihua Jiang","doi":"10.1016/j.jmaa.2025.129810","DOIUrl":"10.1016/j.jmaa.2025.129810","url":null,"abstract":"<div><div>In this paper, we study a density-suppressed motility reaction-diffusion population model with Dirichlet boundary conditions in spatially heterogeneous environments. We establish the existence of local-in-time classical solutions and apply local bifurcation theory to identify a positive bifurcation point for steady-state solutions. The existence of non-constant positive steady-state solutions is obtained, and it is shown that the bifurcation direction of the bifurcation curve can be either forward or backward, which is determined by the density-suppressed diffusion term. Furthermore, the boundedness of non-constant positive steady-state solutions is obtained by the comparison principle, and the boundedness of solutions implies that the bifurcation branches from local bifurcation can be extended globally, hence a global bifurcation diagram is derived rigorously. Finally, numerical simulations verify our theoretical results and demonstrate the effect of spatial heterogeneity on pattern formation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129810"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322874","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":"Infinite divisibility of the product of two correlated normal random variables and exact distribution of the sample mean","authors":"Robert E. Gaunt ,&nbsp;Saralees Nadarajah ,&nbsp;Tibor K. Pogány","doi":"10.1016/j.jmaa.2025.129800","DOIUrl":"10.1016/j.jmaa.2025.129800","url":null,"abstract":"<div><div>We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129800"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314358","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":"Fractal representations of the number zero on the parabola curve","authors":"Xuemin Wang ,&nbsp;Yi Lu ,&nbsp;Jingjing Chen ,&nbsp;Kan Jiang","doi":"10.1016/j.jmaa.2025.129801","DOIUrl":"10.1016/j.jmaa.2025.129801","url":null,"abstract":"<div><div>Motivated by several results in the study of unique <em>q</em>-expansions, this paper investigates the following problem. Let <span><math><mi>K</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> be a self-similar set with the convex hull <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>. How many distinct pairs <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>∈</mo><mi>K</mi></math></span> satisfy the equation<span><span><span><math><mn>0</mn><mo>=</mo><mi>y</mi><mo>−</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>?</mo></math></span></span></span> We establish the following result:</div><div>For any <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and any <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span>, there exists a homogeneous self-similar set <em>K</em> (with convex hull <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>) such that<span><span><span><math><mi>α</mi><mo>−</mo><mi>ϵ</mi><mo>&lt;</mo><msub><mrow><mi>dim</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>K</mi><mo>)</mo><mo>&lt;</mo><mi>α</mi><mo>,</mo></math></span></span></span> and the equation<span><span><span><math><mn>0</mn><mo>=</mo><mi>y</mi><mo>−</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>∈</mo><mi>K</mi><mo>,</mo></math></span></span></span> has exactly countably many distinct solutions. Specifically,<span><span><span><math><mo>{</mo><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mi>y</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>}</mo><mo>∩</mo><mi>K</mi><mo>=</mo><mrow><mo>{</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msup></mrow></mfrac><mo>)</mo></mrow><mo>:</mo><mi>k</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>∪</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>}</mo></mrow><mo>∪</mo><mo>{</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>}</mo><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> denotes the Hausdorff dimension, and <span><math><mn>1</mn><mo>/</mo><mi>m</mi></math></span>, <span><math><mi>m</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, represents the similarity ratio of <em>K</em>. Similar result can be proved for the Bedford-McMullen carpet.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129801"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314359","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":"Zeros of random Müntz polynomials","authors":"Doron S. Lubinsky ,&nbsp;Igor E. Pritsker","doi":"10.1016/j.jmaa.2025.129799","DOIUrl":"10.1016/j.jmaa.2025.129799","url":null,"abstract":"<div><div>We study the expected number of positive zeros of Müntz polynomials with real i.i.d. coefficients. For the standard Gaussian coefficients, we establish asymptotic results for the expected number of positive zeros when the exponents of Müntz monomials that span our random Müntz polynomials have polynomial and logarithmic growth. We also present many bounds on the expected number of zeros of random Müntz polynomials with various real i.i.d. coefficients, including the case of arbitrary nontrivial real i.i.d. coefficients. Since Müntz polynomials include lacunary polynomials, sparse polynomials or fewnomials as special cases, our results directly apply to the expected number of real zeros for those classes of polynomials with gaps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129799"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314467","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":"Algebraic properties of Toeplitz + Hankel operators","authors":"Caixing Gu","doi":"10.1016/j.jmaa.2025.129797","DOIUrl":"10.1016/j.jmaa.2025.129797","url":null,"abstract":"<div><div>Recently an elegant result of Sang <span><span>[29]</span></span> characterizes when the product of two Toeplitz + Hankel operators is a Toeplitz + Hankel operator ((T+H)-operator). This result unifies several product problems for Toeplitz and Hankel operators. We extend the method of the author <span><span>[19]</span></span> on product problems for block Toeplitz and Hankel operators to give a short proof and some refinements of the result of Sang. Furthermore, we identify (T+H)-operators which are isometries or unitaries. We characterize when two arbitrary (T+H)-operators commute. We introduce several classes of (T+H)-operators which extend some classes of (T+H)-operators studied by Basor and Ehrhardt <span><span>[2]</span></span> <span><span>[3]</span></span> and Sang <span><span>[29]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129797"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270216","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 regularity of solutions to a class of nonlocal evolution equations with sectorial operators","authors":"Nguyen Van Dac ,&nbsp;Tran Dinh Ke ,&nbsp;Pham Anh Toan","doi":"10.1016/j.jmaa.2025.129798","DOIUrl":"10.1016/j.jmaa.2025.129798","url":null,"abstract":"<div><div>We deal with an abstract model of nonlocal evolution equations with sectorial operators and nonlinear perturbations. Regularity estimates for resolvent families are derived through semigroup representation, which allow us to show a global solvability for the associated Cauchy problem in fractional power spaces. Employing fixed point argument and resolvent theory, we obtain a Hölder regularity result for the mentioned problem. Then the analytic resolvent theory is utilized to demonstrate that the obtained solution is a strong one under appropriate conditions. An application to a class of nonlinear subdiffusion equations in the whole space is given.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129798"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271349","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":"Shrinking bounded domains to totally bounded ones","authors":"Mihály Bessenyei ,&nbsp;Evelin Pénzes","doi":"10.1016/j.jmaa.2025.129808","DOIUrl":"10.1016/j.jmaa.2025.129808","url":null,"abstract":"<div><div>The Kuratowski measure of noncompactness or the measure of nondensifiability provide direct approach to topological fixed point theorems or to existence issues of generalized fractals. We point out that these measures are not so distinguished as they appear at first glance: Requiring quite simple properties on a set-function, we can prove analogous results. The method behind (the main result of this note) is a reducing principle which allows to shrink bounded and closed domains to compact ones. In the approach, the Knaster–Tarski and the Kantorovich Fixed Point Theorems play a key role.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129808"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314637","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":"A multifractal analysis for uniform level sets with constraints on word appearance","authors":"Ziyu Liu","doi":"10.1016/j.jmaa.2025.129793","DOIUrl":"10.1016/j.jmaa.2025.129793","url":null,"abstract":"<div><div>Given a topologically transitive subshift of finite type, the <em>u</em>-dimension of the level sets of the quotient of Birkhoff sums is a well-studied topic. In this paper, we consider what we shall call the uniform level sets, which are subsets of the level sets. We shall show that the <em>α</em>-level set and the uniform <em>α</em>-level set have the same <em>u</em>-dimension. Moreover, we also consider two types of subsets of the uniform level sets, whose elements satisfy certain constraints on their subwords in addition. We shall show that for <em>α</em> not on the boundary of the dimension spectrum, these subsets of the uniform <em>α</em>-level set also have the same <em>u</em>-dimension as the <em>α</em>-level set. As an application, we shall perform a multifractal analysis of the Hölder regularity of a Gibbs measure on a one-dimensional manifold.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129793"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271348","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}