Pub Date : 2024-12-19DOI: 10.1016/j.aml.2024.109437
Ran Zhang, Xue Ren
This paper considers the global asymptotic stability of a model with epidemic model with high risk and vaccinated class, and extends the related methods to two case of reaction–diffusion equations. The results presented here generalize those from Movahedi (2024).
{"title":"Lyapunov functions for some epidemic model with high risk and vaccinated class","authors":"Ran Zhang, Xue Ren","doi":"10.1016/j.aml.2024.109437","DOIUrl":"10.1016/j.aml.2024.109437","url":null,"abstract":"<div><div>This paper considers the global asymptotic stability of a model with epidemic model with high risk and vaccinated class, and extends the related methods to two case of reaction–diffusion equations. The results presented here generalize those from Movahedi (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109437"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889364","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}
Pub Date : 2024-12-19DOI: 10.1016/j.aml.2024.109433
Ying Li, Yongli Song
In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and global equation. It has been shown that the perceptual radius can destabilize the constant steady state via Turing bifurcation and the critical bifurcation value is theoretically determined.
{"title":"Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel","authors":"Ying Li, Yongli Song","doi":"10.1016/j.aml.2024.109433","DOIUrl":"10.1016/j.aml.2024.109433","url":null,"abstract":"<div><div>In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and global equation. It has been shown that the perceptual radius can destabilize the constant steady state via Turing bifurcation and the critical bifurcation value is theoretically determined.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109433"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889365","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}
Pub Date : 2024-12-19DOI: 10.1016/j.aml.2024.109434
Haoyuan Gong , Tongtong Zhou , Baochang Shi , Rui Du
The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.
{"title":"Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian","authors":"Haoyuan Gong , Tongtong Zhou , Baochang Shi , Rui Du","doi":"10.1016/j.aml.2024.109434","DOIUrl":"10.1016/j.aml.2024.109434","url":null,"abstract":"<div><div>The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109434"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929323","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}
Pub Date : 2024-12-18DOI: 10.1016/j.aml.2024.109428
Ru Meng , Tingting Zheng , Yantao Luo , Zhidong Teng
Using the method of characteristics and defining one auxiliary function, we prove the existence of global attractor for a general age-structured HIV model, which can be used to solve the uniformly persistence problem in the Kumar and Abbas (2022).
{"title":"Global attractor for an age-structured HIV model with nonlinear incidence rate","authors":"Ru Meng , Tingting Zheng , Yantao Luo , Zhidong Teng","doi":"10.1016/j.aml.2024.109428","DOIUrl":"10.1016/j.aml.2024.109428","url":null,"abstract":"<div><div>Using the method of characteristics and defining one auxiliary function, we prove the existence of global attractor for a general age-structured HIV model, which can be used to solve the uniformly persistence problem in the Kumar and Abbas (2022).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109428"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874398","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}
Pub Date : 2024-12-18DOI: 10.1016/j.aml.2024.109430
Jianlun Liu , Hong-Rui Sun , Ziheng Zhang
This paper is concerned with the HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity. After giving a novel proof of subadditivity of the constraint minimizing problem and establishing the Brézis–Lieb lemma for square-root-type nonlinearity, we not only prove the existence of normalized solutions but also give its energy estimate.
{"title":"Normalized solutions to HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity","authors":"Jianlun Liu , Hong-Rui Sun , Ziheng Zhang","doi":"10.1016/j.aml.2024.109430","DOIUrl":"10.1016/j.aml.2024.109430","url":null,"abstract":"<div><div>This paper is concerned with the HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity. After giving a novel proof of subadditivity of the constraint minimizing problem and establishing the Brézis–Lieb lemma for square-root-type nonlinearity, we not only prove the existence of normalized solutions but also give its energy estimate.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109430"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874397","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}
Pub Date : 2024-12-18DOI: 10.1016/j.aml.2024.109432
Wenxv Ding , Ying Li , Musheng Wei
Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through the application of orthogonal matrices. Owing to the utilization of orthogonal transformations, the algorithm exhibits numerical stability. Numerical experiments are provided to illustrate the efficiency of the structure-preserving algorithm.
{"title":"A new structure-preserving method for dual quaternion Hermitian eigenvalue problems","authors":"Wenxv Ding , Ying Li , Musheng Wei","doi":"10.1016/j.aml.2024.109432","DOIUrl":"10.1016/j.aml.2024.109432","url":null,"abstract":"<div><div>Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through the application of orthogonal matrices. Owing to the utilization of orthogonal transformations, the algorithm exhibits numerical stability. Numerical experiments are provided to illustrate the efficiency of the structure-preserving algorithm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109432"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889377","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}
Pub Date : 2024-12-18DOI: 10.1016/j.aml.2024.109431
Weibing Wang, Shen Luo
In this paper, we study the existence of infinitely many positive periodic solutions to a class of second order functional differential equations which cannot be applied directly to the fixed point theorem in cone. With suitable deformations, we construct the operator whose fixed point is closely related to the periodic solution of the original equation and show that the problem has infinitely many positive periodic solutions under appropriate conditions.
{"title":"Infinitely many positive periodic solutions for second order functional differential equations","authors":"Weibing Wang, Shen Luo","doi":"10.1016/j.aml.2024.109431","DOIUrl":"10.1016/j.aml.2024.109431","url":null,"abstract":"<div><div>In this paper, we study the existence of infinitely many positive periodic solutions to a class of second order functional differential equations which cannot be applied directly to the fixed point theorem in cone. With suitable deformations, we construct the operator whose fixed point is closely related to the periodic solution of the original equation and show that the problem has infinitely many positive periodic solutions under appropriate conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109431"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874326","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}
Pub Date : 2024-12-17DOI: 10.1016/j.aml.2024.109427
B. Kazmierczak , V. Volpert
Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of two or more morphogens described by a reaction–diffusion system of equations. In this work we suggest another mechanism of the emergence of spatial distributions in biological tissues based on local cell communication and global inhibition, and described by a nonlocal reaction–diffusion equation. Instability of the homogeneous in space solution leads to the emergence of stationary pulses and not of periodic solutions as in the case of Turing instability.
{"title":"On a new mechanism of the emergence of spatial distributions in biological models","authors":"B. Kazmierczak , V. Volpert","doi":"10.1016/j.aml.2024.109427","DOIUrl":"10.1016/j.aml.2024.109427","url":null,"abstract":"<div><div>Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of two or more morphogens described by a reaction–diffusion system of equations. In this work we suggest another mechanism of the emergence of spatial distributions in biological tissues based on local cell communication and global inhibition, and described by a nonlocal reaction–diffusion equation. Instability of the homogeneous in space solution leads to the emergence of stationary pulses and not of periodic solutions as in the case of Turing instability.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109427"},"PeriodicalIF":2.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874399","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}
We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation with a prescribed mass Here , is a given constant and is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32 (2019), no. 12, 4942–4966] and [Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 174, 43 pp.] for or . After fully utilizing the properties of positive solutions given by Jeanjean,Zhang and Zhong[J. Math. Pures Appl. (9) 183 (2024), 44–75], we give an alternative approach and extend the existence of infinitely many sign-changing normalized solutions to all .
{"title":"Infinitely many sign-changing normalized solutions for nonlinear scalar field equations","authors":"Jiaxin Zhan , Jianjun Zhang , Xuexiu Zhong , Jinfang Zhou","doi":"10.1016/j.aml.2024.109426","DOIUrl":"10.1016/j.aml.2024.109426","url":null,"abstract":"<div><div>We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation <span><span><span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span></span></span>with a prescribed mass <span><math><mrow><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>a</mi><mo>.</mo></mrow></math></span> Here <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow></math></span> is a given constant and <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32 (2019), no. 12, 4942–4966] and [Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 174, 43 pp.] for <span><math><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math></span> or <span><math><mrow><mi>N</mi><mo>≥</mo><mn>6</mn></mrow></math></span>. After fully utilizing the properties of positive solutions given by Jeanjean,Zhang and Zhong[J. Math. Pures Appl. (9) 183 (2024), 44–75], we give an alternative approach and extend the existence of infinitely many sign-changing normalized solutions to all <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109426"},"PeriodicalIF":2.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874400","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}
Pub Date : 2024-12-14DOI: 10.1016/j.aml.2024.109424
Mengxin Chen , Xue-Zhi Li , Canrong Tian
This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state bifurcation and spatial patterns under the attractive type prey-taxis or without prey-taxis.
{"title":"Spatiotemporal dynamics in a three-component predator–prey model","authors":"Mengxin Chen , Xue-Zhi Li , Canrong Tian","doi":"10.1016/j.aml.2024.109424","DOIUrl":"10.1016/j.aml.2024.109424","url":null,"abstract":"<div><div>This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state bifurcation and spatial patterns under the attractive type prey-taxis or without prey-taxis.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109424"},"PeriodicalIF":2.9,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823262","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}
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