Compactness Methods and Nonlinear Hyperbolic Conservation Laws
暂无分享,去创建一个
[1] C. B. Morrey. Multiple Integrals in the Calculus of Variations , 1966 .
[2] J. Holton. Geophysical fluid dynamics. , 1983, Science.
[3] J. Smoller. Shock Waves and Reaction-Diffusion Equations , 1983 .
[4] D. Schaeffer,et al. Riemann problems for nonstrictly hyperbolic 2×2 systems of conservation laws , 1987 .
[5] D. Serre,et al. Linear stability of shock profiles for a rate-type viscoelastic system with relaxation , 1998 .
[6] Entropies and weak solutions of the compressible isentropic Euler equations , 1997 .
[7] P. Lax. Shock Waves and Entropy , 1971 .
[8] R. J. DiPerna. Convergence of approximate solutions to conservation laws , 1983 .
[9] Peizhu Luo,et al. CONVERGENCE OF THE LAX–FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (III) , 1985 .
[10] Tai-Ping Liu. Nonlinear resonance for quasilinear hyperbolic equation , 1987 .
[11] J. J. Stoker. Water Waves: The Mathematical Theory with Applications , 1957 .
[12] Sarah Rothstein. Statistical Thermodynamics Of Nonequilibrium Processes , 2016 .
[13] On E. E. Levi's functions for hyperbolic equations with triple characteristics , 1972 .
[14] ASYMPTOTIC LIMIT OF INITIAL BOUNDARY VALUE PROBLEMS FOR CONSERVATION LAWS WITH RELAXATIONAL EXTENSIONS , 1998 .
[15] Lawrence C. Evans,et al. Weak convergence methods for nonlinear partial differential equations , 1990 .
[16] Rutherford Aris,et al. Theory and application of hyperbolic systems of quasilinear equations , 1989 .
[17] P. D. Lax. Problems Solved and Unsolved Concerning Linear and Nonlinear Partial Differential Equation , 2010 .
[18] Roberto Natalini,et al. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation , 1995 .
[19] Seung-Yeal Ha,et al. L1 Stability for Systems of Hyperbolic Conservation Laws with a Resonant Moving Source , 2003, SIAM J. Math. Anal..
[21] Michael Westdickenberg,et al. Convergence of Approximate Solutions of Conservation Laws , 2015, 1502.00798.
[22] Z. Xin,et al. The relaxation schemes for systems of conservation laws in arbitrary space dimensions , 1995 .
[23] P. Lions. Mathematical topics in fluid mechanics , 1996 .
[24] Gui-Qiang G. Chen,et al. Compressible Euler Equations¶with General Pressure Law , 2000 .
[25] Hyperbolic systems with double characteristics , 1993 .
[26] A. I. Vol'pert. THE SPACES BV AND QUASILINEAR EQUATIONS , 1967 .
[27] L. Chambers. Linear and Nonlinear Waves , 2000, The Mathematical Gazette.
[28] J. Greenberg,et al. Time-periodic solutions to systems of conservation laws , 1991 .
[29] Luc Tartar,et al. Compensated compactness and applications to partial differential equations , 1979 .
[30] R. Natalini. Convergence to equilibrium for the relaxation approximations of conservation laws , 1996 .
[31] Takaaki Nishida,et al. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation , 1979 .
[32] B. Riemann. über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite , 1860 .
[33] Takaaki Nishida,et al. Global solution for an initial boundary value problem of a quasilinear hyperbolic system , 1968 .
[34] J. Glimm. Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .
[35] C. Cercignani. The Boltzmann equation and its applications , 1988 .
[36] C. Papenfuss. Rational Thermodynamics , 2020, Continuum Thermodynamics and Constitutive Theory.
[37] James Glimm,et al. A generalized Riemann problem for quasi-one-dimensional gas flows , 1984 .
[38] David H. Wagner,et al. Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions , 1987 .
[39] Gui-Qiang G. Chen. The method of quasidecoupling for discontinuous solutions to conservation laws , 1992 .
[40] Yong Jung Kim. A MATHEMATICAL INTRODUCTION TO FLUID MECHANICS , 2008 .
[41] S. Friedland,et al. On the Crossing Rule , 1984 .
[42] C. Dafermos. Generalized characteristics in hyperbolic systems of conservation laws , 1989 .
[43] Jian-Guo Liu,et al. Convergence of difference schemes with high resolution for conservation laws , 1997, Math. Comput..
[44] L. Young,et al. Lectures on the Calculus of Variations and Optimal Control Theory. , 1971 .
[45] Applications of the Theory of Compensated Compactness , 1986 .
[46] L. Hörmander. Analysis of Linear Partial Differential Operators II , 2005 .
[47] Gui-Qiang G. Chen. Hyperbolic systems of conservation laws with a symmetry , 1991 .
[48] G. Papanicolaou,et al. The fluid‐dynamical limit of a nonlinear model boltzmann equation , 1979 .
[49] Thomas G. Kurtz. Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics , 1973 .
[50] Y. Meyer,et al. Compensated compactness and Hardy spaces , 1993 .
[51] Gui-Qiang G. Chen,et al. Global solutions to the compressible Euler equations with geometrical structure , 1996 .
[52] E. G.v.. Lectures on the calculus of variations , 1906 .
[53] L. Hörmander,et al. Lectures on Nonlinear Hyperbolic Differential Equations , 1997 .
[54] C. D. Levermore,et al. Moment closure hierarchies for kinetic theories , 1996 .
[55] Tai-Ping Liu. The deterministic version of the Glimm scheme , 1977 .
[56] Charles B. Morrey,et al. QUASI-CONVEXITY AND THE LOWER SEMICONTINUITY OF MULTIPLE INTEGRALS , 1952 .
[57] L. Evans. The perturbed test function method for viscosity solutions of nonlinear PDE , 1989, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[58] F. Murat,et al. Compacité par compensation , 1978 .
[59] J. Nohel,et al. Weak Solutions for a Nonlinear System in Viscoelasticity. , 1988 .
[60] R. J. Diperna,et al. Convergence of the viscosity method for isentropic gas dynamics , 1983 .
[61] Irene M. Gamba. Stationary transonic solutions of a one—dimensional hydrodynamic model for semiconductors , 1992 .
[62] M. Pinsky,et al. Lectures on Random Evolution , 1991 .
[63] Tai-Ping Liu. Quasilinear hyperbolic systems , 1979 .
[64] R. Winther,et al. A system of conservation laws with a relaxation term , 1996 .
[65] L. Tartar. H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations , 1990, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[66] Tai-Ping Liu. L 1 STABILITY FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS , 1999 .
[67] C. Schmeiser,et al. Semiconductor equations , 1990 .
[68] Gui-Qiang G. Chen,et al. The vanishing viscosity method in one-dimensional thermoelasticity , 1995 .
[69] B. Perthame,et al. Kinetic formulation of the isentropic gas dynamics andp-systems , 1994 .
[70] Hermano Frid,et al. Decay of Entropy Solutions of Nonlinear Conservation Laws , 1999 .
[71] J. Ball. A version of the fundamental theorem for young measures , 1989 .
[72] Joel Smoller,et al. Global solutions of the cauchy problem for quasi‐linear first‐order equations in several space variables , 2010 .
[73] Gui-Qiang G. Chen,et al. Hyperbolic conservation laws with umbilic degeneracy, I , 1995 .
[74] P. Lax. Hyperbolic systems of conservation laws II , 1957 .
[75] Athanasios E. Tzavaras,et al. Materials with Internal Variables and Relaxation to Conservation Laws , 1999 .
[76] Luc Tartar,et al. The Compensated Compactness Method Applied to Systems of Conservation Laws , 1983 .
[77] K. Trivisa. A prior1 estimates in hyperbolic systems of conservation laws via generalized characteristics , 1997 .
[78] Richard Courant,et al. Supersonic Flow And Shock Waves , 1948 .
[79] D. Serre. La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d'espace , 1986 .
[80] B. Perthame,et al. Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics , 1998 .
[81] Ingo Müller,et al. Molecular Extended Thermodynamics , 1993 .
[82] Gui-Qiang G. Chen,et al. Zero relaxation and dissipation limits for hyperbolic conservation laws , 1993 .
[83] Gui-Qiang G. Chen,et al. Hyperbolic Conservation Laws with Umbilic Degeneracy II , 2022 .
[84] Pierre Degond,et al. On a one-dimensional steady-state hydrodynamic model , 1990 .
[85] P. Lax. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .
[86] Constantine M. Dafermos,et al. Applications of the invariance principle for compact processes II. Asymptotic behavior of solutions of a hyperbolic conservation law , 1972 .
[87] Tai-Ping Liu. Nonlinear stability and instability of transonic flows through a nozzle , 1982 .
[88] François Murat. Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant , 1981 .
[89] S. Ukai,et al. The global weak solutions of compressible Euler equation with spherical symmetry , 1992 .
[90] Fluid Dynamic Limits of Discrete Velocity Kinetic Equations , 1991 .
[91] Hermano Frid,et al. Divergence‐Measure Fields and Hyperbolic Conservation Laws , 1999 .
[92] Constantine M. Dafermos,et al. Hyperbolic Systems of Conservation Laws , 1983 .
[93] A. Majda,et al. Multiple Steady States for 1-D Transonic Flow , 1984 .
[94] L. Cesari,et al. Contributions to modern calculus of variations , 1987 .
[95] A. Bressan,et al. Uniqueness of Weak Solutions to Systems of Conservation Laws , 1997 .
[96] Michael Struwe,et al. Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems , 1990 .
[97] T. G. Cowling,et al. The mathematical theory of non-uniform gases : notes added in 1951 , 1951 .
[98] P. Souganidis,et al. Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates , 1998 .
[99] V. S. Vladimirov,et al. Equations of mathematical physics , 1972 .
[100] H. Glaz,et al. The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow , 1984 .
[101] Tai-Ping Liu. Hyperbolic conservation laws with relaxation , 1987 .
[102] Gui-Qiang G. Chen,et al. Convergence of shock capturing schemes for the compressible Euler-Poisson equations , 1996 .
[103] Bernard Dacorogna,et al. Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals , 1982 .
[104] S. Yau,et al. Lectures on Differential Geometry , 1994 .
[105] Gui-Qiang G. Chen,et al. Large-Time Behavior of Entropy Solutions of Conservation Laws☆ , 1999 .
[106] P. Lax. The multiplicity of eigenvalues , 1982 .
[107] C. D. Levermore,et al. Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms , 1996 .
[108] David G. Schaeffer,et al. The classification of 2 × 2 systems of non‐strictly hyperbolic conservation laws, with application to oil recovery , 1987 .
[109] Shock capturing approximations to the compressible Euler equations with geometric structure and related equations , 1998 .
[110] C. D. Levermore,et al. Hyperbolic conservation laws with stiff relaxation terms and entropy , 1994 .
[111] M. Froissart. Hyperbolic equations and waves : Battelle Seattle 1968 Recontres , 1970 .