Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity

From MaRDI portal
Publication:1239437

DOI10.1007/BF00251584zbMath0361.35046OpenAlexW2058382538MaRDI QIDQ1239437

Thomas J. R. Hughes, Tosio Kato, Jerrold E. Marsden

Publication date: 1977

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251584



Related Items

Global existence of small solutions to a class of nonlinear evolution equations, Boundary determination for an inverse problem in elastodynamics, Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in $3+1$ dimensions, Relativistic elasticity II *, Unnamed Item, ANALYTICAL APPROACHES TO CHARGE TRANSPORT IN A MOVING MEDIUM, Thermoelasticity with second sound?exponential stability in linear and non-linear 1-d, On solutions to some quasilinear hyperbolic equations with nonlinear inhomogeneous terms, On the wave propagation property in finite elasticity, Global existence and nonexistence results for a class of semilinear hyperbolic systems, Evolution equations governed by quasilinear operators satisfying Carathéodory’s conditions, Parabolic Approximation of Quasilinear Wave Equations with Applications in Nonlinear Acoustics, Trigonometric integrators for quasilinear wave equations, Causal geometry of rough Einstein CMCSH spacetime, Discretization of time-dependent quantum systems: real-time propagation of the evolution operator, Causal dissipation in the relativistic dynamics of barotropic fluids, Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions, Unnamed Item, Using the Navier-Cauchy equation for motion estimation in dynamic imaging, Characteristic gluing to the Kerr family and application to spacelike gluing, Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations, A product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equations, Sharp local well-posedness for quasilinear wave equations with spherical symmetry, Global stability of traveling waves for (1 + 1)-dimensional systems of quasilinear wave equations, Semilinear wave equations on accelerated expanding FLRW spacetimes, Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022, Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions, A class of Hadamard well-posed five-field theories of dissipative relativistic fluid dynamics, One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations, A causal formulation of dissipative relativistic fluid dynamics with or without diffusion, On optimal control for linear distributed time-delay systems, Low regularity ill-posedness for elastic waves driven by shock formation, The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions, The time-like minimal surface equation in Minkowski space: low regularity solutions, Unnamed Item, Low regularity local solutions for field equations, Long time existence and singular perturbation results for quasi-linear hyperbolic equations with small parameter and dissipation term, The resolution of the bounded \(L^2\) curvature conjecture in general relativity, The resolution of the bounded \(L^2\) curvature conjecture in general relativity, Causal dissipation for the relativistic dynamics of ideal gases, A class of hyperbolic volterra integrodifferential equations, Cauchy-Born rule and the stability of crystalline solids: dynamic problems, Stability for second order abstract evolution equations, Extension or blow up of classical solutions to quasilinear evolution equations in banach spaces, On the radius of injectivity of null hypersurfaces, Formation of singularities in one-dimensional thermoelasticity with second sound, On the breakdown criterion in general relativity, Cauchy Problem for Nonlinear Hyperbolic Systems of Partial Differential Equations, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III, On local uniqueness in nonlinear elastodynamics, Degeneracy in Finite Time of 1D Quasilinear Wave Equations, Causal non-stationary thermodynamics of non-viscous heat conducting fluids with internal variables, On potential wells and stability in nonlinear elasticity, On the well-posedness of relativistic viscous fluids with non-zero vorticity, Rough solutions of the Einstein constraint equations, Uniqueness in Inverse Problems for Elastic Media with Residual Stress, Local well-posedness of a quasilinear wave equation, Quasi-linear evolution equations in non-reflexive banach spaces, I, A new continuum model for general relativistic viscous heat-conducting media, Peeling or not peeling—is that the question?, Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials, Well posedness in the C∞ class for utt=a(u)Δu, Formation of singularities for a family of 1D quasilinear wave equations, Local existence with low regularity for the 2D compressible Euler equations, LOCAL EXISTENCE AND BLOW UP IN NONLINEAR THERMOELASTICITY WITH SECOND SOUND, Semidirect Products and Reduction in Mechanics, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, The Cauchy problem in extended supergravity, \(N=1\), \(d=11\), The general relativistic constraint equations, Visco-elastodynamics at large strains Eulerian, Neumann boundary feedback stabilization for a nonlinear wave equation: A strict \(H^2\)-Lyapunov function, The initial-value problem for elastodynamics of incompressible bodies, On a local existence theorem for quasilinear hyperbolic mixed problems with Neumann type boundary conditions, A local existence and uniqueness theorem for a K-BKZ-fluid, A functional analytic approach to uniqueness of solutions to some nonlinear Cauchy problems, Determination of the spacetime from local time measurements, Detection of Hermitian connections in wave equations with cubic non-linearity, Geodesics and the Einstein nonlinear wave system, Cauchy problem for the Kuznetsov equation, A solvability result for a nonlinear weakly hyperbolic equation of second order, Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations, Well-posedness for mutational equations under a general type of dissipativity conditions, The incompressible limit in nonlinear elasticity, On a local existence theorem of Neumann problem for some quasilinear hyperbolic system of 2nd order, Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2. (Existence for an elasto-dynamic nonlinear Neumann problem in two dimensions), Global solutions and blow-up solutions for a nonlinear string with boundary input and output, An existence theorem for the Dirichlet problem in the elastodynamics of incompressible materials, A geometric approach for sharp local well-posedness of quasilinear wave equations, Instability phenomena and adiabatic shear band localization in termoplastic flow processes, Degeneracy in finite time of 1D quasilinear wave equations. II, Local existence of solutions of self gravitating relativistic perfect fluids, On stationary solutions of two-dimensional Euler equation, The bounded \(L^2\) curvature conjecture, On \({(W_2^1(\mathbb R)\cap W_\infty^1(\mathbb R))}\)-solutions of the equation \({u_{tt}=(a(u)u_x)_x+f(x,t)}\), The abstract Cauchy problem for dissipative operators with respect to metric-like functionals, Hyperbolic methods for Einstein's equations, A mixed problem for quasilinear impulsive hyperbolic equations with non stationary boundary and transmission conditions, A high-order discontinuous Galerkin method for nonlinear sound waves, Justification of the Cauchy-Born approximation of elastodynamics, Geodesics and the Einstein-nonlinear wave system., Global solutions of the evolutionary Faddeev model with small initial data, Global solutions to systems of quasilinear wave equations with low regularity data and applications, The boost problem in general relativity, Energy criteria for finite hyperelasticity, On the mathematical foundations of elastic stability theory. I, New integral estimates for deformations in terms of their nonlinear strains, Generalized solutions to semilinear elliptic PDE with applications to the Lichnerowicz equation, Nonlinear responses from the interaction of two progressing waves at an interface, Space-times of low differentiability and singularities, Solution globale des équations de Maxwell-Dirac-Klein-Gordon, Local in time existence for the complete Maxwell equations with monotone characteristic in a bounded domain, On the well-posedness of the vacuum Einstein's equations, Asynchronous multi-domain variational integrators for nonlinear hyperelastic solids, Global existence and asymptotic behavior for one-dimensional thermoelasticity of integral type with hyperbolic heat conduction, On maximal globally hyperbolic vacuum space-times, Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations, The Dirichlet-Cauchy problem for nonlinear hyperbolic equations in a domain with edges, Local properties of an isothermal charged fluid: Initial-boundary value problem, Residual-based shock capturing in solids, Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type, On the motion of a compact elastic body, Deformations of incompressible bodies with free boundaries, Rough solutions of Einstein vacuum equations in CMCSH gauge, Mutational analysis with transitions whose domains vary in state and that are not necessarily Lipschitz continuous in time, Asymptotic stability of homogeneous states in the relativistic dynamics of viscous, heat-conductive fluids, Mathematical general relativity, Well-posedness of the equations of generalized thermoelasticity, Global solutions to quasi-linear hyperbolic systems of viscoelasticity, The Cauchy problem for quasi-linear Schrödinger equations, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Conformal wave equations for the Einstein-tracefree matter system, A new Hamiltonian structure for the dynamics of general relativity, Some applications of geometry in continuum mechanics, Space-time \(L^{2}\) estimates, regularity and almost global existence for elastic waves, Nonlinear interaction of waves in elastodynamics and an inverse problem, Well-posedness of the hydrostatic MHD equations, On anisotropic compressible materials that can sustain elastodynamic anti-plane shear, A review on some contributions to perturbation theory, singular limits and well-posedness, Energy minimization and the formation of microstructure in dynamic anti- plane shear, Formation of singularities in solutions of a wave equation, The existence of solution to the finite elastodynamics with mixed boundary conditions, Stability of relative equilibria. II: Application to nonlinear elasticity, Coarse graining holographic black holes, An inverse problem in elastodynamics: Uniqueness of the wave speeds in the interior, Interaction of deformation waves and localization phenomena in inelastic solids, Rough solutions of the 3-D compressible Euler equations, Approximation of abstract Cauchy problems for dissipative operators with respect to metric-like functionals, Global solutions of abstract quasi-linear evolution equations of ``hyperbolic type, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion, Quasilinear hyperbolic and parabolic systems: Contractive semidiscretizations and convergence of the discrete viscosity method, The existence of local semiflows for nonlinear differential equations in Banach spaces, and applications to partial differential equations, On a boundary integral solution of a lateral planar Cauchy problem in elastodynamics, Analysis of finite element methods for the nonlinear dynamic analysis of shells, Invariant manifolds in mechanics. II. Zero-dimensional elastic bodies with directors, Hyperbolicity of the 3+1 system of Einstein equations, Quasiconvexity at the boundary, positivity of the second variation and elastic stability, Rough solutions of the Einstein vacuum equations, Inverse problem for Einstein-scalar field equations, Weakly regular \(T^2\)-symmetric spacetimes. The global geometry of future Cauchy developments, On global solutions in one-dimensional thermoelasticity with second sound in the half line, Localized fracture phenomena in thermo-visco-plastic flow processes under cyclic dynamic loadings., Mixed problems for fully nonlinear hyperbolic equations, Continuum and discrete initial-boundary value problems and Einstein's field equations, Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics, Global stability of solutions to nonlinear wave equations



Cites Work