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Journal of Hyperbolic Differential Equations最新文献

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On the initial-boundary value problem for the Euler equations in presence of a rarefaction wave 存在稀疏波时欧拉方程的初边值问题
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-08-21 DOI: 10.1142/S0219891619500103
Dening Li
{"title":"On the initial-boundary value problem for the Euler equations in presence of a rarefaction wave","authors":"Dening Li","doi":"10.1142/S0219891619500103","DOIUrl":"https://doi.org/10.1142/S0219891619500103","url":null,"abstract":"We study the initial-boundary value problem for the general non-isentropic 3D Euler equations with data which are incompatible in the classical sense, but are “rarefaction-compatible”. We show that such data are also rarefaction-compatible of infinite order and the initial-boundary value problem has a piece-wise smooth solution containing a rarefaction wave.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41533874","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
Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions 一类二维非齐次非线性Schrödinger方程的能量散射
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-08-08 DOI: 10.1142/S0219891621500016
Van Duong Dinh
{"title":"Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions","authors":"Van Duong Dinh","doi":"10.1142/S0219891621500016","DOIUrl":"https://doi.org/10.1142/S0219891621500016","url":null,"abstract":"We consider a class of [Formula: see text]-supercritical inhomogeneous nonlinear Schrödinger equations in two dimensions [Formula: see text] where [Formula: see text] and [Formula: see text]. Using a new approach of Arora et al. [Scattering below the ground state for the 2D radial nonlinear Schrödinger equation, Proc. Amer. Math. Soc. 148 (2020) 1653–1663], we show the energy scattering for the equation with radially symmetric initial data. In the focusing case, our result extends the one of Farah and Guzmán [Scattering for the radial focusing INLS equation in higher dimensions, Bull. Braz. Math. Soc. (N.S.) 51 (2020) 449–512] to the whole range of [Formula: see text] where the local well-posedness is available. In the defocusing case, our result extends the one in [V. D. Dinh, Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, J. Evol. Equ. 19(2) (2019) 411–434], where the energy scattering for non-radial initial data was established in dimensions [Formula: see text].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44235971","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: 13
Singular limits of the quasi-linear Kolmogorov-type equation with a source term 具有源项的拟线性kolmogorov型方程的奇异极限
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-07-09 DOI: 10.1142/s0219891621500247
I. Kuznetsov, S. Sazhenkov
{"title":"Singular limits of the quasi-linear Kolmogorov-type equation with a source term","authors":"I. Kuznetsov, S. Sazhenkov","doi":"10.1142/s0219891621500247","DOIUrl":"https://doi.org/10.1142/s0219891621500247","url":null,"abstract":"Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with the Kolmogorov-type, genuinely nonlinear, degenerate hyperbolic–parabolic (ultra-parabolic) equation with a smooth source term is established. In addition, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is investigated and the formal limit is rigorously justified. Our proofs rely on the use of kinetic equations and the compensated compactness method for genuinely nonlinear balance laws.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47692344","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
The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings 具有Poisson或Helmholtz耦合的可压缩Euler系统的全局存在性问题
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-06-19 DOI: 10.1142/s0219891621500041
vS'arka Nevcasov'a, X. Blanc, R. Danchin, B. Ducomet, andvs Nevcasov'a
{"title":"The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings","authors":"vS'arka Nevcasov'a, X. Blanc, R. Danchin, B. Ducomet, andvs Nevcasov'a","doi":"10.1142/s0219891621500041","DOIUrl":"https://doi.org/10.1142/s0219891621500041","url":null,"abstract":"We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference vector field [Formula: see text] such that the spectrum of [Formula: see text] is positive and bounded away from zero. We prove the existence of a global unique solution with (fractional) Sobolev regularity, and algebraic time decay estimates. Our work extends Grassin and Serre’s papers [Existence de solutions globales et régulières aux équations d’Euler pour un gaz parfait isentropique, C. R. Acad. Sci. Paris Sér. I 325 (1997) 721–726, 1997; Global smooth solutions to Euler equations for a perfect gas, Indiana Univ. Math. J. 47 (1998) 1397–1432; Solutions classiques globales des équations d’Euler pour un fluide parfait compressible, Ann. Inst. Fourier Grenoble 47 (1997) 139–159] dedicated to the compressible Euler system without coupling and with integer regularity exponents.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41824939","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: 6
Discontinuous viscosity solutions of first-order Hamilton–Jacobi equations 一阶Hamilton–Jacobi方程的间断粘性解
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-06-13 DOI: 10.1142/s0219891621500259
Michiel Bertsch, Flavia Smarrazzo, A. Terracina, A. Tesei
{"title":"Discontinuous viscosity solutions of first-order Hamilton–Jacobi equations","authors":"Michiel Bertsch, Flavia Smarrazzo, A. Terracina, A. Tesei","doi":"10.1142/s0219891621500259","DOIUrl":"https://doi.org/10.1142/s0219891621500259","url":null,"abstract":"We study the Cauchy problem for the simplest first-order Hamilton–Jacobi equation in one space dimension, with a bounded and Lipschitz continuous Hamiltonian which only depends on the spatial derivative. Uniqueness of discontinuous viscosity solutions is proven, if the initial data function has a finite number of jump discontinuities. Main ingredients of the proof are the barrier effect of spatial discontinuities of a solution (which is linked to the boundedness of the Hamiltonian), and a comparison theorem for semicontinuous viscosity subsolution and supersolution. These are defined in the spirit of the paper [H. Ishii, Perron’s method for Hamilton–Jacobi equations, Duke Math. J. 55 (1987) 368–384], yet using essential limits to introduce semicontinuous envelopes. The definition is shown to be compatible with Perron’s method for existence and is crucial in the uniqueness proof. We also describe some properties of the time evolution of spatial jump discontinuities of the solution, and obtain several results about singular Neumann problems which arise in connection with the above referred barrier effect.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48637170","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: 3
Optimal jump set in hyperbolic conservation laws 双曲守恒律中的最优跳集
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-06-05 DOI: 10.1142/S021989162050023X
Shyam Sundar Ghoshal, A. Jana
{"title":"Optimal jump set in hyperbolic conservation laws","authors":"Shyam Sundar Ghoshal, A. Jana","doi":"10.1142/S021989162050023X","DOIUrl":"https://doi.org/10.1142/S021989162050023X","url":null,"abstract":"We investigate qualitative properties of entropy solutions to hyperbolic conservation laws, and construct an entropy solution to a scalar conservation law for which the jump set is not closed, in particular, it is dense in a space-time domain. In a second part, we establish a similar result for hyperbolic systems. We give two different approaches for scalar conservation laws and hyperbolic systems in order to obtain these results. For the scalar case, the solutions are explicitly calculated.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46170965","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
Diffusion models for mixtures using a stiff dissipative hyperbolic formalism 使用刚性耗散双曲形式的混合物扩散模型
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-06-01 DOI: 10.1142/S0219891619500115
L. Boudin, Bérénice Grec, V. Pavan
{"title":"Diffusion models for mixtures using a stiff dissipative hyperbolic formalism","authors":"L. Boudin, Bérénice Grec, V. Pavan","doi":"10.1142/S0219891619500115","DOIUrl":"https://doi.org/10.1142/S0219891619500115","url":null,"abstract":"We consider a system of fluid equations for mixtures with a stiff relaxation term of Maxwell–Stefan diffusion type. We use the formalism developed by Chen et al. and derive a limiting system of Fick type, in which the species velocities tend to align with a bulk velocity when the relaxation parameter remains small.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500115","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41544912","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: 3
On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function 具有一般通量函数的双曲平衡律系统的BV熵解的结构
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-06-01 DOI: 10.1142/S0219891619500139
F. Ancona, L. Caravenna, A. Marson
{"title":"On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function","authors":"F. Ancona, L. Caravenna, A. Marson","doi":"10.1142/S0219891619500139","DOIUrl":"https://doi.org/10.1142/S0219891619500139","url":null,"abstract":"The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension, Comm. Partial Differential Equations 39(2) (2014) 244–273] for strictly hyperbolic system of conservation laws.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41810919","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
Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2 波导上散焦三次Schrödinger方程的全局适定性和散射ℝ2×𝕋2.
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-05-24 DOI: 10.1142/S0219891619500048
Zehua Zhao
{"title":"Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ℝ2 × 𝕋2","authors":"Zehua Zhao","doi":"10.1142/S0219891619500048","DOIUrl":"https://doi.org/10.1142/S0219891619500048","url":null,"abstract":"We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on [Formula: see text]. This equation is critical both at the level of energy and mass. The key ingredients are global-in-time Stricharz estimate, resonant system approximation, profile decomposition and energy induction method. Assuming the large data scattering for the 2d cubic resonant system, we prove the large data scattering for this problem. This problem is the cubic analogue of a problem studied by Hani and Pausader.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500048","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48360873","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: 7
Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state 具有非线性平衡态的Boltzmann-Poisson系统的扩散极限
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-05-24 DOI: 10.1142/S021989161950005X
Lanoir Addala, M. L. Tayeb
{"title":"Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state","authors":"Lanoir Addala, M. L. Tayeb","doi":"10.1142/S021989161950005X","DOIUrl":"https://doi.org/10.1142/S021989161950005X","url":null,"abstract":"The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S021989161950005X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41766717","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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