The Cauchy problem for quasi-linear symmetric hyperbolic systems

1975/01/01 by Tosio Kato · 39 citations
Mathematics · #advanced mathematical theories #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics

paper · doi:10.1007/bf00280740

Cited by

• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
• On the Equations of Compressible Fluid Dynamics With Cattaneo‐Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure
• Lifespan Bounds and Super-Classical Propagation for Weak Solutions of the Three-Dimensional Compressible Euler Equations
• Pseudo-magnetic Fields and Effective Dynamics in Strained Honeycomb Structures
• From nonisothermal BGK to Euler Maxwellians via relative entropy
• Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations
• Relaxation Limit in Besov Spaces for Compressible Euler Equations
• Operator splitting for dispersion-generalized Benjamin-Ono equations
• A kinetic transport-projection splitting algorithm for an hierarchy of moment closures of gas-kinetic equations
• On Kato-Sobolev spaces. The Wiener-Lévy theorem for Kato-Sobolev algebras H_\mathttul^s
• Large-time behavior of solutions to the outflow problem for the compressible Navier-Stokes-Maxwell equations
• From bipolar Euler-Poisson system to unipolar Euler-Poisson system in the perspective of mass
• Formation of singularity for compressible viscoelasticity
• Well-posedness of compressible Euler equations in a physical vacuum
• Global Existence and Asymptotic Equivalence to Barenblatt-type Solutions for the Physical Vacuum Free Boundary Problem of Damped Compressible Euler Equations in M-D
• Global existence and large time behavior for the system of compressible adiabatic flow through porous media in ℝ³
• A note on relations between convexity and concavity of thermodynamic functions
• Keller-Osserman and Harnack type results for nonlinear elliptic PDE with unbounded ingredients
• Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices
• An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle
• The global classical solution to compressible Euler system with velocity alignment
• Well-Posedness for the Euler-Nordstrom System with Cosmological Constant
• Global well-posedness of the compressible bipolar Euler-Maxwell system in R³
• Einstein's equation and geometric asymptotics
• The Euler-Maxwell two-fluid system in 3D
• W-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds
• Acoustic Limit for the Boltzmann equation in Optimal Scaling
• Homogenization of Randomly Deformed Conductivity Resistant Membranes
• Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model
• Global Solution to the Vacuum Free Boundary Problem with Physical Singularity of Compressible Euler Equations with Damping and Gravity
• The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics
• Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
• Front Tracking for Scalar Conservation Laws with Spatially Heterogeneous Flux
• Well-Posedness of the Einstein-Euler System in Asymptotically Flat Spacetimes
• STABILITY AND INSTABILITY OF EXPANDING SOLUTIONS TO THE LORENTZIAN CONSTANT-POSITIVE-MEAN-CURVATURE FLOW
• Error estimate for time-explicit finite volume approximation of strong\n solutions to systems of conservation laws
• Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations. [europepmc]
• Conformal geodesics and the evolution of spacetimes with positive Cosmological constant. [europepmc]
• Cosmologies with positive λ: hierarchies of future behaviour. [europepmc]