Pub Date : 2025-02-22DOI: 10.1016/j.aml.2025.109506
Fan Wu
This note investigates the formation of singularities for the 3D Navier–Stokes equations. By employing a bilinear estimate and a logarithmic interpolation inequality, we derive a new extension criterion based on two vorticity components in Vishik-type spaces, which refines several previously established results concerning Navier–Stokes equations.
{"title":"Remarks on Navier–Stokes regularity criteria in Vishik-type spaces","authors":"Fan Wu","doi":"10.1016/j.aml.2025.109506","DOIUrl":"10.1016/j.aml.2025.109506","url":null,"abstract":"<div><div>This note investigates the formation of singularities for the 3D Navier–Stokes equations. By employing a bilinear estimate and a logarithmic interpolation inequality, we derive a new extension criterion based on two vorticity components in Vishik-type spaces, which refines several previously established results concerning Navier–Stokes equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109506"},"PeriodicalIF":2.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474114","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 : 2025-02-22DOI: 10.1016/j.aml.2025.109507
Biao Liu , Wan-Tong Li , Wen-Bing Xu
This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe that certain components may manifest as propagating terraces with multiple steps, while others exhibit single-front profiles under specific conditions, but it is also possible for all components to display single-front profiles, depending on the selection of coefficients. Furthermore, we prove that the solutions tend to flatten as the spatial propagation has infinite speed.
{"title":"Propagating terrace with infinite speed in cooperative systems with multiple types of diffusions","authors":"Biao Liu , Wan-Tong Li , Wen-Bing Xu","doi":"10.1016/j.aml.2025.109507","DOIUrl":"10.1016/j.aml.2025.109507","url":null,"abstract":"<div><div>This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe that certain components may manifest as propagating terraces with multiple steps, while others exhibit single-front profiles under specific conditions, but it is also possible for all components to display single-front profiles, depending on the selection of coefficients. Furthermore, we prove that the solutions tend to flatten as the spatial propagation has infinite speed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109507"},"PeriodicalIF":2.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474115","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 : 2025-02-21DOI: 10.1016/j.aml.2025.109505
Ruiwen Wu , Zhiting Xu
This paper is devoted to investigate a discrete Nicholson’s blowflies model with two delays. We construct some novel upper and lower solutions for the wave equation and then show the equation admits the traveling wave fronts connecting two equilibria of the associated spatially homogeneous system. And also, we obtain the non-existence for traveling waves of the model.
{"title":"Traveling wave fronts for a discrete Nicholson’s blowflies model with two delays","authors":"Ruiwen Wu , Zhiting Xu","doi":"10.1016/j.aml.2025.109505","DOIUrl":"10.1016/j.aml.2025.109505","url":null,"abstract":"<div><div>This paper is devoted to investigate a discrete Nicholson’s blowflies model with two delays. We construct some novel upper and lower solutions for the wave equation and then show the equation admits the traveling wave fronts connecting two equilibria of the associated spatially homogeneous system. And also, we obtain the non-existence for traveling waves of the model.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109505"},"PeriodicalIF":2.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471144","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 : 2025-02-20DOI: 10.1016/j.aml.2025.109504
Yanli Huang, Guo Lin
This paper is concerned with the minimal wave speed of exclusion traveling wave solutions in a delayed competitive systems. Because of the intraspecific delays, the system cannot generate monotone semiflows. We give the minimal wave speed by combining different recipes. Here, the minimal wave speed is linearly determinate.
{"title":"Minimal wave speed of competitive diffusive systems with time delays","authors":"Yanli Huang, Guo Lin","doi":"10.1016/j.aml.2025.109504","DOIUrl":"10.1016/j.aml.2025.109504","url":null,"abstract":"<div><div>This paper is concerned with the minimal wave speed of exclusion traveling wave solutions in a delayed competitive systems. Because of the intraspecific delays, the system cannot generate monotone semiflows. We give the minimal wave speed by combining different recipes. Here, the minimal wave speed is linearly determinate.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109504"},"PeriodicalIF":2.9,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465250","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 : 2025-02-19DOI: 10.1016/j.aml.2025.109503
Juan Kang, Yao Cheng
Balanced-norm error bounds have been established in Cheng et al. (2022) for the local discontinuous Galerkin (LDG) method using alternating numerical flux on Shishkin-type meshes. However, the convergence rate is shown to be one-half order lower than the numerical results in the general case. This paper seeks to fill up this gap by introducing a new composite projector in the error analysis. We achieve an optimal-order error estimate in the balanced-norm for the LDG method on both Shishkin-type and Bakhvalov-type meshes, uniformly in the small perturbation parameter.
{"title":"Optimal-order balanced-norm error estimate of the local discontinuous Galerkin method with alternating numerical flux for singularly perturbed reaction–diffusion problems","authors":"Juan Kang, Yao Cheng","doi":"10.1016/j.aml.2025.109503","DOIUrl":"10.1016/j.aml.2025.109503","url":null,"abstract":"<div><div>Balanced-norm error bounds have been established in Cheng et al. (2022) for the local discontinuous Galerkin (LDG) method using alternating numerical flux on Shishkin-type meshes. However, the convergence rate is shown to be one-half order lower than the numerical results in the general case. This paper seeks to fill up this gap by introducing a new composite projector in the error analysis. We achieve an optimal-order error estimate in the balanced-norm for the LDG method on both Shishkin-type and Bakhvalov-type meshes, uniformly in the small perturbation parameter.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109503"},"PeriodicalIF":2.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454989","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 : 2025-02-18DOI: 10.1016/j.aml.2025.109502
Zixin Zhang, Q.P. Liu
A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. 146 (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits -peakon solution, is shown to be a flow of the integrable hierarchy related to the celebrated Burgers equation.
{"title":"On a two-component Camassa–Holm equation","authors":"Zixin Zhang, Q.P. Liu","doi":"10.1016/j.aml.2025.109502","DOIUrl":"10.1016/j.aml.2025.109502","url":null,"abstract":"<div><div>A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. <strong>146</strong> (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits <span><math><mi>N</mi></math></span>-peakon solution, is shown to be a flow of the integrable hierarchy related to the celebrated Burgers equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109502"},"PeriodicalIF":2.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454988","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 : 2025-02-18DOI: 10.1016/j.aml.2025.109501
He Zhang, Haibo Chen
<div><div>In this paper, we investigate the Hartree–Fock type system: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>u</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>λ</mi><mi>v</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>v</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow><mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>|</mo></mrow></mrow></mfrac><mi>d</mi><mi>y</mi><mo>,</mo></mrow></math></span> the parameters <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ρ</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. Such a system is regarded as an approximation of the Coulomb system of two particles that occurs in quantum mechanics. Due to the existence of the nonlocal term <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub></math></span>, we find that in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, the energy of the minimizer is bounded in the radial case but not in the non-radial case. To further investigate this phenomenon, without loss of generality, we consider the problem in a ball <span><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi><
{"title":"Existence and behavior of minimizers for a class of Hartree–Fock type systems","authors":"He Zhang, Haibo Chen","doi":"10.1016/j.aml.2025.109501","DOIUrl":"10.1016/j.aml.2025.109501","url":null,"abstract":"<div><div>In this paper, we investigate the Hartree–Fock type system: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>u</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>λ</mi><mi>v</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>v</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow><mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>|</mo></mrow></mrow></mfrac><mi>d</mi><mi>y</mi><mo>,</mo></mrow></math></span> the parameters <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ρ</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. Such a system is regarded as an approximation of the Coulomb system of two particles that occurs in quantum mechanics. Due to the existence of the nonlocal term <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub></math></span>, we find that in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, the energy of the minimizer is bounded in the radial case but not in the non-radial case. To further investigate this phenomenon, without loss of generality, we consider the problem in a ball <span><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi><","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109501"},"PeriodicalIF":2.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437894","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 : 2025-02-15DOI: 10.1016/j.aml.2025.109500
Yingying Xie
We construct in this paper an efficient spectral Galerkin approximation in combination with scalar auxiliary variable (SAV) method to the Allen–Cahn model and Cahn–Hilliard model in polar geometry. Since the spectral methods cannot be directly applied to the non-rectangular regions, the disk region is firstly mapped to the rectangular region by the polar transformation that will lead to singularity at the pole, then providing appropriate pole conditions and basis functions are fundamental for constructing efficient algorithms. Moreover, the accuracy and stability of the proposed approximation are verified by numerical experiments.
{"title":"The efficient spectral Galerkin method to the phase-field models in polar geometry","authors":"Yingying Xie","doi":"10.1016/j.aml.2025.109500","DOIUrl":"10.1016/j.aml.2025.109500","url":null,"abstract":"<div><div>We construct in this paper an efficient spectral Galerkin approximation in combination with scalar auxiliary variable (SAV) method to the Allen–Cahn model and Cahn–Hilliard model in polar geometry. Since the spectral methods cannot be directly applied to the non-rectangular regions, the disk region is firstly mapped to the rectangular region by the polar transformation that will lead to singularity at the pole, then providing appropriate pole conditions and basis functions are fundamental for constructing efficient algorithms. Moreover, the accuracy and stability of the proposed approximation are verified by numerical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109500"},"PeriodicalIF":2.9,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429905","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 : 2025-02-14DOI: 10.1016/j.aml.2025.109499
Mengze Guo, Shaojie Yang
In this paper, we study solitary waves for the geophysical Green–Naghdi (gGN) system which describing the propagation of large amplitude surface waves. We give a description of the solitary wave profiles by performing a phase-plane analysis, and present explicit solitary wave solutions. The results reveal the influence of the relationship between the Coriolis parameter and wave speed on the existence of solitary waves.
{"title":"Effects of the Coriolis effect on solitary waves of the geophysical Green–Naghdi system","authors":"Mengze Guo, Shaojie Yang","doi":"10.1016/j.aml.2025.109499","DOIUrl":"10.1016/j.aml.2025.109499","url":null,"abstract":"<div><div>In this paper, we study solitary waves for the geophysical Green–Naghdi (gGN) system which describing the propagation of large amplitude surface waves. We give a description of the solitary wave profiles by performing a phase-plane analysis, and present explicit solitary wave solutions. The results reveal the influence of the relationship between the Coriolis parameter and wave speed on the existence of solitary waves.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109499"},"PeriodicalIF":2.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418581","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 : 2025-02-13DOI: 10.1016/j.aml.2025.109498
Quanguo Zhang
In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in D’Abbicco (2014). Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral inequality.
{"title":"Nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms","authors":"Quanguo Zhang","doi":"10.1016/j.aml.2025.109498","DOIUrl":"10.1016/j.aml.2025.109498","url":null,"abstract":"<div><div>In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in D’Abbicco (2014). Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral inequality.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109498"},"PeriodicalIF":2.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418586","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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