发布求助
文献互助 智能选刊 最新文献

Journal of Hyperbolic Differential Equations最新文献

筛选
英文 中文
Well and ill-posedness of free boundary problems to relativistic Euler equations 相对论欧拉方程自由边界问题的好问题和坏问题
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-09-01 DOI: 10.1142/s0219891623500169
Yongcai Geng
{"title":"Well and ill-posedness of free boundary problems to relativistic Euler equations","authors":"Yongcai Geng","doi":"10.1142/s0219891623500169","DOIUrl":"https://doi.org/10.1142/s0219891623500169","url":null,"abstract":"In this paper, via the regularity of sonic speed, we are concerned with the well and ill-posedness problems of the relativistic Euler equations with free boundary. First, we deduce the physical vacuum condition of relativistic Euler equations, which means that the sonic speed [Formula: see text] behaves like a half power of distance to the vacuum boundary [Formula: see text], satisfying [Formula: see text], it belongs to H[Formula: see text]lder continuous. Then, for [Formula: see text], this case means that the sonic speed belongs to [Formula: see text] smooth across the vacuum boundary, it is proved from both Lagrangian and Eulerian coordinates points of view. Finally, for the cases [Formula: see text] and [Formula: see text], the boundary behaviors are verified ill-posed by the unbounded acceleration of the fluid near the vacuum boundary. In this paper, the uniform bounds of velocity [Formula: see text] with respect to [Formula: see text] and the upper bounds for the square of sonic speed [Formula: see text] are very important in the proof of no matter whether well or ill-posedness because this will enable us to avoid many difficulties in the mathematical structure of relativistic fluids especially near the vacuum boundary. It is our innovation that distinguishes from non-relativistic Euler equations [J. Jang and N. Masmoudi, Well and ill-posedness for compressible Euler equations with vacuum, J. Math. Phys. 53 (2012) 1–11].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139343411","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
A two-component nonlinear variational wave system 双分量非线性变分波系
4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-09-01 DOI: 10.1142/s0219891623500182
Peder Aursand, Anders Nordli
{"title":"A two-component nonlinear variational wave system","authors":"Peder Aursand, Anders Nordli","doi":"10.1142/s0219891623500182","DOIUrl":"https://doi.org/10.1142/s0219891623500182","url":null,"abstract":"We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time. We prove that a special semilinear case is globally well-posed. We show that a particular long time asymptotic expansion around a constant state in a moving frame satisfies the two-component Hunter–Saxton system.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894829","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
Sharp a-contraction estimates for small extremal shocks 对小的极端冲击的急剧收缩估计
4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-09-01 DOI: 10.1142/s0219891623500170
William Golding, Sam Krupa, Alexis Vasseur
{"title":"Sharp a-contraction estimates for small extremal shocks","authors":"William Golding, Sam Krupa, Alexis Vasseur","doi":"10.1142/s0219891623500170","DOIUrl":"https://doi.org/10.1142/s0219891623500170","url":null,"abstract":"In this paper, we study the [Formula: see text]-contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected to large perturbations. We show that the weight coefficient [Formula: see text] can be chosen with amplitude proportional to the size of the shock. The main result of this paper is a key building block in the companion paper [G. Chen, S. G. Krupa and A. F. Vasseur, Uniqueness and weak-BV stability for [Formula: see text] conservation laws, Arch. Ration. Mech. Anal. 246(1) (2022) 299–332] in which uniqueness and BV-weak stability results for [Formula: see text] systems of hyperbolic conservation laws are proved.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894813","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: 4
Temple system on networks 网络上的寺庙系统
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-09-01 DOI: 10.1142/s0219891623500200
R. Borsche, M. Garavello, B. Gunarso
{"title":"Temple system on networks","authors":"R. Borsche, M. Garavello, B. Gunarso","doi":"10.1142/s0219891623500200","DOIUrl":"https://doi.org/10.1142/s0219891623500200","url":null,"abstract":"This paper deals with the well-posedness on a network of a Temple system of nonlinear hyperbolic balance laws. Temple systems are characterized by the fact that shock and rarefaction curves coincide. This study is motivated by a model for traffic, recently proposed, inspired by kinetic considerations. The proof of the well-posedness is based on the wave-front tracking procedure, on the pseudo-polygonal technique and on the operator splitting method.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"40 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139344934","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
Kolmogorov continuity and stability of sample paths of entropy solutions of stochastic conservation laws 随机守恒律熵解样本路径的Kolmogorov连续性和稳定性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-06-01 DOI: 10.1142/s0219891623500091
Suprio Bhar, Imran H. Biswas, Saibal Khan, G. Vallet
{"title":"Kolmogorov continuity and stability of sample paths of entropy solutions of stochastic conservation laws","authors":"Suprio Bhar, Imran H. Biswas, Saibal Khan, G. Vallet","doi":"10.1142/s0219891623500091","DOIUrl":"https://doi.org/10.1142/s0219891623500091","url":null,"abstract":"This paper is concerned with sample paths and path-based properties of the entropy solution to conservation laws with stochastic forcing. We derive a series of uniform maximal-type estimates for the viscous perturbation and establish the existence of stochastic entropy solution that has Hölder continuous sample paths. This information is then carefully choreographed with Kružkov’s technique to obtain stronger continuous dependence estimates, based on the nonlinearities, for the sample paths of the solutions. Finally, convergence of sample paths is established for vanishing viscosity approximation along with an explicit rate of convergence.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49082178","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 with exponential singularity for (3 + 1)-D Protter problems （3+1）-D Proter问题的指数奇异解
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-06-01 DOI: 10.1142/s0219891623500145
N. Popivanov, T. Popov, I. Witt
{"title":"Solutions with exponential singularity for (3 + 1)-D Protter problems","authors":"N. Popivanov, T. Popov, I. Witt","doi":"10.1142/s0219891623500145","DOIUrl":"https://doi.org/10.1142/s0219891623500145","url":null,"abstract":"In the 1950s, Protter proposed multi-dimensional analogues of the classical Guderley–Morawetz problem for mixed-type hyperbolic-elliptic equations on the plane that models transonic flows in fluid dynamics. The multi-dimensional variants turn out to be different from the two-dimensional case and the situation there is still not clear. Here, we study Protter problems in the hyperbolic part of the domain. Unlike the planar analogues, the four-dimensional variant is not well-posed for classical solutions. The problem is not Fredholm — there is an infinite number of necessary conditions for classical solvability. Alternatively, the notion of a generalized solution that may have singularities was introduced. It is known that for smooth right-hand sides, the uniquely determined generalized solution may have a power-type growth at one boundary point. The singularity is isolated at the vertex of the boundary characteristic light cone and does not propagate along the cone. Here, we construct a new singular solution with an exponential growth at the point where the singularity appears.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49657726","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
Peeling-off behavior of wave equation in the Vaidya spacetime 波动方程在Vaidya时空中的剥离行为
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-06-01 DOI: 10.1142/s021989162350011x
Armand Coudray
{"title":"Peeling-off behavior of wave equation in the Vaidya spacetime","authors":"Armand Coudray","doi":"10.1142/s021989162350011x","DOIUrl":"https://doi.org/10.1142/s021989162350011x","url":null,"abstract":"We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason–Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterized by Sobolev-type norms, in terms of corresponding function spaces of initial data. All function spaces are obtained from energy fluxes associated with an observer constructed from the Morawetz vector field on Minkowski spacetime. We combine conformal techniques and energy estimates to obtain the optimal classes of initial data ensuring a given regularity of the rescaled field. The classes of data are equivalent to those obtained on Minkowski and Schwarzschild spacetimes in that they impose the same decay at infinity and regularity.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46538302","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
Shock profiles of Navier–Stokes equations for compressible medium 可压缩介质Navier-Stokes方程的冲击剖面
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-06-01 DOI: 10.1142/s0219891623500157
Chueh-Hsin Chang, Tai-Ping Liu
{"title":"Shock profiles of Navier–Stokes equations for compressible medium","authors":"Chueh-Hsin Chang, Tai-Ping Liu","doi":"10.1142/s0219891623500157","DOIUrl":"https://doi.org/10.1142/s0219891623500157","url":null,"abstract":"We construct the viscous profile of the Navier–Stokes equations for compressible media under certain sufficient local hypotheses of the constitutive relation. Our result applies to shocks of arbitrary strength and generalizes the classical work of Gilbarg for the convex constitutive relation of Bethe–Weyl.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44815793","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
Convergence to a diffusive contact wave for solutions to a system of hyperbolic balance laws 双曲平衡律系统解的扩散接触波收敛性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-03-01 DOI: 10.1142/s0219891623500078
Yanni Zeng
{"title":"Convergence to a diffusive contact wave for solutions to a system of hyperbolic balance laws","authors":"Yanni Zeng","doi":"10.1142/s0219891623500078","DOIUrl":"https://doi.org/10.1142/s0219891623500078","url":null,"abstract":"We consider a [Formula: see text] system of hyperbolic balance laws that is the converted form under inverse Hopf–Cole transformation of a Keller–Segel type chemotaxis model. We study Cauchy problem when Cauchy data connect two different end-states as [Formula: see text]. The background wave is a diffusive contact wave of the reduced system. We establish global existence of solution and study the time asymptotic behavior. In the special case where the cellular population initially approaches its stable equilibrium value as [Formula: see text], we obtain nonlinear stability of the diffusive contact wave under smallness assumption. In the general case where the population initially does not approach to its stable equilibrium value at least at one of the far fields, we use a correction function in the time asymptotic ansatz, and show that the population approaches logistically to its stable equilibrium value. Our result shows two significant differences when comparing to Euler equations with damping. The first one is the existence of a secondary wave in the time asymptotic ansatz. This implies that our solutions converge to the diffusive contact wave slower than those of Euler equations with damping. The second one is that the correction function logistically grows rather than exponentially decays.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46622178","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
The non-uniqueness of admissible solutions to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint 具有最大密度约束的可压缩等熵欧拉系统二维Riemann问题可容许解的非唯一性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2023-03-01 DOI: 10.1142/s0219891623500017
J. Hua, Lirong Xia
{"title":"The non-uniqueness of admissible solutions to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint","authors":"J. Hua, Lirong Xia","doi":"10.1142/s0219891623500017","DOIUrl":"https://doi.org/10.1142/s0219891623500017","url":null,"abstract":"We investigate the uniqueness of entropy solution to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint. The constraint is imposed with a singular pressure. Given initial data for which the standard self-similar solution consists of one shock or one shock and one rarefaction wave, it turns out that there exist infinitely many admissible weak solutions. This extends the result of Markfelder and Klingenberg in [S. Markfelder and C. Klingenberg, The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock, Arch. Ration. Mech. Anal. 227(3) (2018) 967–994] for classical Euler system to the case with maximum density constraint. Also some estimates on the density of these solutions are given to describe the behavior of solutions near congestion.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45680105","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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信