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Stability of backward-in-time semilinear coupled parabolic systems
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-13 DOI: 10.1016/j.jmaa.2025.129240
Salah-Eddine Chorfi , Masahiro Yamamoto
{"title":"Stability of backward-in-time semilinear coupled parabolic systems","authors":"Salah-Eddine Chorfi ,&nbsp;Masahiro Yamamoto","doi":"10.1016/j.jmaa.2025.129240","DOIUrl":"10.1016/j.jmaa.2025.129240","url":null,"abstract":"<div><div>We consider backward problems for semilinear coupled parabolic systems in bounded domains. We prove conditional stability estimates for linear and semilinear systems of strongly coupled parabolic equations involving general semilinearities. The proof of the stability estimates relies on a modified method by Carleman estimates incorporating the simple weight function <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>λ</mi><mi>t</mi></mrow></msup></math></span> with a sufficiently large parameter <em>λ</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"545 2","pages":"Article 129240"},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143148182","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
The regularity of semi-hyperbolic patches of solutions to the two-dimensional compressible Euler equations in magnetohydrodynamics
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-13 DOI: 10.1016/j.jmaa.2025.129242
Jianjun Chen, Yuqi Zhang, Shuangrong Li
{"title":"The regularity of semi-hyperbolic patches of solutions to the two-dimensional compressible Euler equations in magnetohydrodynamics","authors":"Jianjun Chen,&nbsp;Yuqi Zhang,&nbsp;Shuangrong Li","doi":"10.1016/j.jmaa.2025.129242","DOIUrl":"10.1016/j.jmaa.2025.129242","url":null,"abstract":"<div><div>The semi-hyperbolic patches appear frequently in solutions of multi-dimensional Riemann problem and transonic flow problems. We have obtained a semi-hyperbolic patch solution for the two-dimensional compressible magnetohydrodynamic equations (Chen and Geng, 2019 <span><span>[4]</span></span>). Subsequently, we prove the semi-hyperbolic patch solution is smooth up to the sonic curve and sonic curve is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> continuous (Chen and Geng, 2020 <span><span>[5]</span></span>). This paper will further consider the regularity of semi-hyperbolic patch problem to the two-dimensional compressible Euler equations in magnetohydrodynamics. By constructing an appropriate variable and using characteristic decomposition and bootstrap method, we show that the semi-hyperbolic patch solution is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></msup></math></span> up to the sonic curve and sonic curve is also <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"545 2","pages":"Article 129242"},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143148184","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
On the resolvent convergence of discrete Dirac operators on 3D cubic lattices
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-13 DOI: 10.1016/j.jmaa.2025.129247
Karl Michael Schmidt , Tomio Umeda
{"title":"On the resolvent convergence of discrete Dirac operators on 3D cubic lattices","authors":"Karl Michael Schmidt ,&nbsp;Tomio Umeda","doi":"10.1016/j.jmaa.2025.129247","DOIUrl":"10.1016/j.jmaa.2025.129247","url":null,"abstract":"<div><div>We prove that the discrete Dirac operators in three dimensions converge to the continuum Dirac operators in the strong resolvent sense, but not in the norm resolvent sense.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129247"},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131248","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
Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-13 DOI: 10.1016/j.jmaa.2025.129244
Benoît F. Sehba
{"title":"Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers","authors":"Benoît F. Sehba","doi":"10.1016/j.jmaa.2025.129244","DOIUrl":"10.1016/j.jmaa.2025.129244","url":null,"abstract":"<div><div>We define two notions of Logarithmic Bloch space in the polydisc for which we provide equivalent definitions in terms of symbols of bounded Hankel operators. We also provide a full characterization of the pointwise multipliers between two different Bloch spaces of the unit polydisc.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 1","pages":"Article 129244"},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166520","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
Convolution powers of unbounded measures on the positive half-line
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129232
Dariusz Buraczewski , Alexander Iksanov , Alexander Marynych
{"title":"Convolution powers of unbounded measures on the positive half-line","authors":"Dariusz Buraczewski ,&nbsp;Alexander Iksanov ,&nbsp;Alexander Marynych","doi":"10.1016/j.jmaa.2025.129232","DOIUrl":"10.1016/j.jmaa.2025.129232","url":null,"abstract":"<div><div>For a right-continuous nondecreasing and unbounded function <em>V</em> of at most exponential growth, which vanishes on the negative half-line, we investigate the asymptotic behavior of the Lebesgue-Stieltjes convolution powers <span><math><msup><mrow><mi>V</mi></mrow><mrow><mo>⁎</mo><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo></math></span> as both <em>j</em> and <em>t</em> tend to infinity. We obtain a comprehensive asymptotic formula for <span><math><msup><mrow><mi>V</mi></mrow><mrow><mo>⁎</mo><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, which is valid across different regimes of simultaneous growth of <em>j</em> and <em>t</em>. Our main technical tool is an exponential change of measure, which is a standard technique in the large deviations theory. Various applications of our result are given.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129232"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164648","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
On the fractal dimensions of continuous functions and algebraic genericity
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129234
Jia Liu, Yuan Zhang, Saisai Shi
{"title":"On the fractal dimensions of continuous functions and algebraic genericity","authors":"Jia Liu,&nbsp;Yuan Zhang,&nbsp;Saisai Shi","doi":"10.1016/j.jmaa.2025.129234","DOIUrl":"10.1016/j.jmaa.2025.129234","url":null,"abstract":"<div><div>In this paper, we consider the algebraic genericity of continuous functions in terms of Hausdorff and box dimensions. More precisely, we show that, given <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></math></span>, the set of functions <span><math><mi>f</mi><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> whose graphs have box and Hausdorff dimensions <em>s</em> everywhere in the unit interval is maximal-dense-lineable and also dense-algebrable. This work answers affirmatively two questions of Bonilla et al. (2019) <span><span>[15]</span></span>. In addition, we consider the algebraic genericity of continuous functions whose level sets satisfy some dimensional properties.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129234"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165888","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
Lattice Lipschitz superposition operators on Banach function spaces
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129233
Roger Arnau , Jose M. Calabuig , Ezgi Erdoğan , Enrique A. Sánchez Pérez
{"title":"Lattice Lipschitz superposition operators on Banach function spaces","authors":"Roger Arnau ,&nbsp;Jose M. Calabuig ,&nbsp;Ezgi Erdoğan ,&nbsp;Enrique A. Sánchez Pérez","doi":"10.1016/j.jmaa.2025.129233","DOIUrl":"10.1016/j.jmaa.2025.129233","url":null,"abstract":"<div><div>We analyze and characterize the notion of lattice Lipschitz operator when defined between Banach function spaces. After showing some general results, we restrict our attention to the case of those Lipschitz operators which are representable by pointwise composition with a strongly measurable function. Mimicking the classical definition and characterizations of (linear) multiplication operators between Banach function spaces, we show that under certain conditions the requirement for a diagonal Lipschitz operator to be well-defined between two such spaces <span><math><mi>X</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> and <span><math><mi>Y</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> is that it can be represented by a strongly measurable function which belongs to the Bochner space <span><math><mi>M</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>(</mo><mi>μ</mi><mo>,</mo><mi>L</mi><mi>i</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>)</mo></math></span>. Here, <span><math><mi>M</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> is the space of multiplication operators between <span><math><mi>X</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> and <span><math><mi>Y</mi><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, and <span><math><mi>L</mi><mi>i</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is the space of real-valued Lipschitz maps with real variable that are equal to 0 in 0. This opens the door to a better understanding of these maps, as well as finding the relation of these operators to some normed tensor products and other classes of maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129233"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164646","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
The estimate for the Lebesgue measure of preimages of iterates of an interval map
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129230
Hongfei Cui
{"title":"The estimate for the Lebesgue measure of preimages of iterates of an interval map","authors":"Hongfei Cui","doi":"10.1016/j.jmaa.2025.129230","DOIUrl":"10.1016/j.jmaa.2025.129230","url":null,"abstract":"<div><div>For an interval map <em>T</em> with two indifferent fixed points, we provide both asymptotic estimates and error bounds for the Lebesgue measure of sets of the form <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>, where <span><math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo><mo>⊂</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. Two concise proofs are presented. The first follows from Heersink's result on the Farey map directly. The second use techniques from infinite ergodic theory along with an effective version of Karamata's Tauberian theorem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129230"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165780","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
Closed ideals of operators on the Baernstein and Schreier spaces
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129235
Niels Jakob Laustsen, James Smith
{"title":"Closed ideals of operators on the Baernstein and Schreier spaces","authors":"Niels Jakob Laustsen,&nbsp;James Smith","doi":"10.1016/j.jmaa.2025.129235","DOIUrl":"10.1016/j.jmaa.2025.129235","url":null,"abstract":"<div><div>We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> for <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> and the <em>p</em>-convexified Schreier spaces <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> for <span><math><mn>1</mn><mo>⩽</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>. Our main conclusion is that there are <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span> many closed ideals that lie between the ideals of compact and strictly singular operators on each of these spaces, and also <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span> many closed ideals that contain projections of infinite rank.</div><div>Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the classical Schreier space <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and its higher-order variants play a key role in the proofs, as does the Johnson–Schechtman technique for constructing <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span> many closed ideals of operators on a Banach space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129235"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165890","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
Weighted bi-parameter fractional Leibniz rules
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-01-10 DOI: 10.1016/j.jmaa.2025.129237
Elizabeth Hale , Virginia Naibo
{"title":"Weighted bi-parameter fractional Leibniz rules","authors":"Elizabeth Hale ,&nbsp;Virginia Naibo","doi":"10.1016/j.jmaa.2025.129237","DOIUrl":"10.1016/j.jmaa.2025.129237","url":null,"abstract":"<div><div>Fractional Leibniz rules are estimates in norm for fractional differential operators applied to the product of functions, resembling the product rule from early calculus. We obtain fractional Leibniz rules associated to partial fractional differential operators and bi-parameter Coifman–Meyer multiplier operators in the setting of weighted Lebesgue spaces, improving the range of the fractional orders of differentiation allowed in existing estimates. Our methods of proof rely on appropriate paraproduct decompositions of bilinear operators and new Nikol'skiĭ representations for weighted bi-parameter Triebel–Lizorkin spaces. As a bi-product, we also obtain bi-parameter fractional Leibniz rule in the context of Triebel–Lizorkin and Besov spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 1","pages":"Article 129237"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167400","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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