Case study of a nonlinear, nonconservative, nonstrictly hyperbolic system

DOI10.1016/0362-546X(92)90030-IzbMath0790.35065OpenAlexW2010894792MaRDI QIDQ4030892

Michael Oberguggenberger

Publication date: 1 April 1993

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(92)90030-i

zbMATH Keywords

existenceuniquenessnonlinear elasticityRiemann problemCauchy problemsgeneralized functionsfunctions with bounded variationparabolic approximationsnonlinear, nonconservative, nonstrictly hyperbolic systemone-dimensional elastic and visco-elastic material of high density

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Nonlinear elasticity (74B20) Initial value problems for first-order hyperbolic systems (35L45) Dynamical problems in solid mechanics (74Hxx)

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Limiting behavior of scaled general Euler equations of compressible fluid flow, Interactions of delta shock waves in a strictly hyperbolic system of conservation laws, Vanishing viscosity limit for a system of balance laws with general type initial data arising from 1D Saint-Venant model, Generalized solutions of the Vlasov-Poisson system with singular data, Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities, Higher order asymptotic for Burgers equation and adhesion model, Interactions of delta shock waves for the transport equations with split delta functions, Generalized solutions to partial differential equations of evolution type, The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory, Burgers equation with a passive scalar: Dissipation anomaly and Colombeau calculus

Cites Work

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• Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations
• Generalized solutions to Burgers' equation
• Generalized solutions to nonlinear first-order systems
• Plane waves in nonlinear electromagnetism
• The elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions
• On a hyperbolic system with a compatible quadratic
• Borel's theorem for generalized functions
• Multiplications of distributions in elasticity and hydrodynamics
• Microscopic Profiles of Shock Waves and Ambiguities in Multiplications of Distributions
• Generalized Solutions to the Korteweg–de Vries and the Regularized Long-Wave Equations
• Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form
• THE SPACES $ BV$ AND QUASILINEAR EQUATIONS
• A wave-interaction model for the generation of windrows
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics
• Weak solutions of nonlinear hyperbolic equations and their numerical computation