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Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux Gurtin-Pipkin通量多孔热弹性系统的指数稳定性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-28 DOI: 10.58997/ejde.2023.44
Jianghao Hao, Jing Yang
{"title":"Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux","authors":"Jianghao Hao, Jing Yang","doi":"10.58997/ejde.2023.44","DOIUrl":"https://doi.org/10.58997/ejde.2023.44","url":null,"abstract":"In this article, we study the stability of a porous thermoelastic system with Gurtin-Pipkin flux. Under suitable assumptions for the derivative of the heat flux relaxation kernel, we establish the existence and uniqueness of solution by applying the semigroup theory, and prove the exponential stability of system without considering the wave velocity by the means of estimates of the resolvent","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49104401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Solutions of complex nonlinear functional equations including second order partial differential and difference in C^2 C^2中包含二阶偏微分和差分的复非线性函数方程的解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-26 DOI: 10.58997/ejde.2023.43
H. Xu, Goutam Haldar
{"title":"Solutions of complex nonlinear functional equations including second order partial differential and difference in C^2","authors":"H. Xu, Goutam Haldar","doi":"10.58997/ejde.2023.43","DOIUrl":"https://doi.org/10.58997/ejde.2023.43","url":null,"abstract":"This article is devoted to exploring the existence and the form of finite order transcendental entire solutions of Fermat-type second order partial differential-difference equations $$ Big(frac{partial^2 f}{partial z_1^2}+deltafrac{partial^2 f}{partial z_2^2} +etafrac{partial^2 f}{partial z_1partial z_2}Big)^2 +f(z_1+c_1,z_2+c_2)^2=e^{g(z_1,z_2)} $$ and $$ Big(frac{partial^2 f}{partial z_1^2}+deltafrac{partial^2 f}{partial z_2^2} +etafrac{partial^2 f}{partial z_1partial z_2}Big)^2+(f(z_1+c_1,z_2+c_2) -f(z_1,z_2))^2=e^{g(z)}, $$ where (delta,etainmathbb{C}) and (g(z_1,z_2)) is a polynomial in (mathbb{C}^2). Our results improve the results of Liu and Dong [23] Liu et al. [24] and Liu and Yang [25] Several examples confirm that the form of tr","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41530039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Viscosity solutions to the infinity Laplacian equation with lower terms 无穷低项拉普拉斯方程的粘度解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-25 DOI: 10.58997/ejde.2023.42
Cuicui Li, Fang Liu
{"title":"Viscosity solutions to the infinity Laplacian equation with lower terms","authors":"Cuicui Li, Fang Liu","doi":"10.58997/ejde.2023.42","DOIUrl":"https://doi.org/10.58997/ejde.2023.42","url":null,"abstract":"We establish the existence and uniqueness of viscosity solutions tothe Dirichlet problem $$displaylines{ Delta_infty^h u=f(x,u), quad hbox{in } Omega,cr u=q, quadhbox{on }partialOmega,}$$ where (qin C(partialOmega)), (h>1), (Delta_infty^h u=|Du|^{h-3}Delta_infty u). The operator (Delta_infty u=langle D^2uDu,Du rangle) is the infinity Laplacian which is strongly degenerate, quasilinear and it is associated with the absolutely minimizing Lipschitz extension. When the nonhomogeneous term (f(x,t)) is non-decreasing in (t), we prove the existence of the viscosity solution via Perron's method. We also establish a uniqueness result based on the perturbation analysis of the viscosity solutions. If the function (f(x,t)) is nonpositive (nonnegative) and non-increasing in (t), we also give the existence of viscosity solutions by an iteration technique under the condition that the domain has small diameter. Furthermore, we investigate the existence and uniqueness of viscosity solutions to the boundary-value problem with singularity $$displaylines{ Delta_infty^h u=-b(x)g(u), quad hbox{in } Omega, cr u>0, quad hbox{in } Omega, cr u=0, quad hbox{on }partialOmega, }$$ when the domain satisfies some regular condition. We analyze asymptotic estimates for the viscosity solution near the boundary.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42021349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Space-time decay rates of a two-phase flow model with magnetic field in R^3 磁场作用下R^3两相流模型的时空衰减率
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-23 DOI: 10.58997/ejde.2023.41
Qin Ye, Yinghui Zhang
{"title":"Space-time decay rates of a two-phase flow model with magnetic field in R^3","authors":"Qin Ye, Yinghui Zhang","doi":"10.58997/ejde.2023.41","DOIUrl":"https://doi.org/10.58997/ejde.2023.41","url":null,"abstract":"We investigate the space-time decay rates of strong solution to a two-phase flow model with magnetic field in the whole space (mathbb{R}^3 ). Based on the temporal decay results by Xiao [24] we show that for any integer (ellgeq 3), the space-time decay rate of (k(0leq k leq ell))-order spatial derivative of the strong solution in the weighted Lebesgue space ( L_gamma^2 ) is (t^{-frac{3}{4}-frac{k}{2}+gamma}). Moreover, we prove that the space-time decay rate of (k(0leq k leq ell-2))-order spatial derivative of the difference between two velocities of the fluid in the weighted Lebesgue space ( L_gamma^2 ) is (t^{-frac{5}{4}-frac{k}{2}+gamma}), which is faster than ones of the two velocities themselves.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41782775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Reduction principle for partial functional differential equation without compactness 不具有紧致性的偏泛函微分方程的约简原理
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-20 DOI: 10.58997/ejde.2023.39
Meryem El Attaouy, K. Ezzinbi, Gaston Mandata ˜N'Guerekata
{"title":"Reduction principle for partial functional differential equation without compactness","authors":"Meryem El Attaouy, K. Ezzinbi, Gaston Mandata ˜N'Guerekata","doi":"10.58997/ejde.2023.39","DOIUrl":"https://doi.org/10.58997/ejde.2023.39","url":null,"abstract":"This article establishes a reduction principle for partial functional differential equation without compactness of the semigroup generated by the linear part. Under conditions more general than the compactness of the C0-semigroup generated by the linear part, we establish the quasi-compactness of the C0-semigroup associated to the linear part of the partial functional differential equation. This result allows as to construct a reduced system that is posed by an ordinary differential equation posed in a finite dimensional space. Through this result we study the existence of almost automorphic and almost periodic solutions for partial functional differential equations. For illustration, we study a transport model.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45321327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Principal eigenvalues for the fractional p-Laplacian with unbounded sign-changing weights 权无界变号分数阶p-拉普拉斯算子的主特征值
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-19 DOI: 10.58997/ejde.2023.38
Oumarou Asso, M. Cuesta, J. Doumatè, L. Leadi
{"title":"Principal eigenvalues for the fractional p-Laplacian with unbounded sign-changing weights","authors":"Oumarou Asso, M. Cuesta, J. Doumatè, L. Leadi","doi":"10.58997/ejde.2023.38","DOIUrl":"https://doi.org/10.58997/ejde.2023.38","url":null,"abstract":"Let (Omega) be a bounded regular domain of ( mathbb{R}^N), (Ngeqslant 1), (pin (1,+infty)), and ( sin (0,1) ). We consider the eigenvalue problem $$displaylines{ (-Delta_p)^s u + V|u|^{p-2}u= lambda m(x)|u|^{p-2}u quadhbox{in } Omega cr u=0 quad hbox{in } mathbb{R}^N setminus Omega, }$$ where the potential V and the weight m are possibly unbounded and are sign-changing. After establishing the boundedness and regularity of weak solutions, we prove that this problem admits principal eigenvalues under certain conditions. We also show that when such eigenvalues exist, they are simple and isolated in the spectrum of the operator.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47017322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals 时间尺度上具有Delta-HK和Delta-HKP积分的混合型积分微分方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-06-15 DOI: 10.58997/ejde.2023.29
A. Sikorska-Nowak
{"title":"Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals","authors":"A. Sikorska-Nowak","doi":"10.58997/ejde.2023.29","DOIUrl":"https://doi.org/10.58997/ejde.2023.29","url":null,"abstract":"In this article we prove the existence of solutions to the integrodifferential equation of mixed type begin{gather*}x^Delta (t)=f Big( t,x(t), int_0^t k_1 (t,s)g(s,x(s)) Delta s, int_0^a k_2(t,s)h(s,x(s)) Delta s Big),cr x(0)=x_0, quad x_0 in E,; t in I_a=[0,a] cap mathbb{T},; a>0, end{gather*} where (mathbb{T}) denotes a time scale (nonempty closed subset of real numbers (mathbb{R})), (I_a) is a time scale interval. In the first part of this paper functions (f,g,h) are Caratheodory functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil delta integrals, which generalizes the Henstock-Kurzweil integrals. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis delta integrals. Additionally, functions f, g, h satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46715677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundedness, stability and pattern formation for a predator-prey model with Sigmoid functional response and prey-taxis 具有Sigmoid功能反应和猎物趋同性的捕食-被捕食模型的有界性、稳定性和模式形成
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-05-04 DOI: 10.58997/ejde.2023.37
Zhihong Zhao, Huanqin Hu
{"title":"Boundedness, stability and pattern formation for a predator-prey model with Sigmoid functional response and prey-taxis","authors":"Zhihong Zhao, Huanqin Hu","doi":"10.58997/ejde.2023.37","DOIUrl":"https://doi.org/10.58997/ejde.2023.37","url":null,"abstract":"This article concerns the structure of the nonconstant steady states for a predator-prey model of Leslie-Gower type with Sigmoid functional and prey-taxis subject to the homogeneous Neumann boundary condition. The existence of bounded classical global solutions is discussed in bounded domains with arbitrary spatial dimension and any prey-taxis sensitivity coefficient. The local stability of the homogeneous steady state is analyzed to show that the prey-taxis sensitivity coefficient destabilizes the stability of the homogeneous steady state when prey defends. Then we study the existence and stability of the nonconstant positive steady state of the system over 1D domain by applying the bifurcation theory and present properties of local branches such as pitchfork and turning direction. Moreover, we discuss global bifurcation, homogeneous steady state solutions, nonconstant steady states solutions, spatio-temporal periodic solutions and spatio-temporal irregular solutions which demonstrate the coexistence and spatial distribution of prey and predator species. Finally, we perform numerical simulations to illustrate and support our theoretical analysis.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47270899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Asymptotic behavior of stochastic functional differential evolution equation 随机泛函微分演化方程的渐近性质
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-04-12 DOI: 10.58997/ejde.2023.35
Jason Clark, Oleksandr Misiats, V. Mogylova, Oleksandr Stanzhytskyi
{"title":"Asymptotic behavior of stochastic functional differential evolution equation","authors":"Jason Clark, Oleksandr Misiats, V. Mogylova, Oleksandr Stanzhytskyi","doi":"10.58997/ejde.2023.35","DOIUrl":"https://doi.org/10.58997/ejde.2023.35","url":null,"abstract":"In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a priory uniform in time bounds for the solutions in the appropriate Hilbert spaces. These bounds enable us to establish the existence of invariant measure based on Krylov-Bogoliubov theorem on the tightness of the family of measures. Finally, under certain assumptions on nonlinearities, we establish the uniqueness of invariant measures.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42465534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Pseudo almost periodicity for stochastic differential equations in infinite dimensions 无限维随机微分方程的伪概周期性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-04-10 DOI: 10.58997/ejde.2023.34
Ye-Jun Chen, H. Ding
{"title":"Pseudo almost periodicity for stochastic differential equations in infinite dimensions","authors":"Ye-Jun Chen, H. Ding","doi":"10.58997/ejde.2023.34","DOIUrl":"https://doi.org/10.58997/ejde.2023.34","url":null,"abstract":"In this article, we introduce the concept of p-mean θ-pseudo almost periodic stochastic processes, which is slightly weaker than p-mean pseudo almost periodic stochastic processes. Using the operator semigroup theory and stochastic analysis theory, we obtain the existence and uniqueness of square-mean θ-pseudo almost periodic mild solutions for a semilinear stochastic differential equation in infinite dimensions. Moreover, we prove that the obtained solution is also pseudo almost periodic in path distribution. It is noteworthy that the ergodic part of the obtained solution is not only ergodic in square-mean but also ergodic in path distribution. Our main results are even new for the corresponding stochastic differential equations (SDEs) in finite dimensions.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44699148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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