On a hyperbolic system with a compatible quadratic

DOI10.1080/03605309908820711zbMath0711.35028OpenAlexW2047876285MaRDI QIDQ3496600

J. François Colombeau, Michael Oberguggenberger

Publication date: 1990

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908820711

zbMATH Keywords

measuressemilinear hyperbolic systemmultiplication of distributionsdelta wave solutions

Mathematics Subject Classification ID

Related Items (21)

Singular solutions of a fully nonlinear 2 × 2 system of conservation laws ⋮ Generalized solutions to a Cauchy problem for a nonconservative hyperbolic system ⋮ Colombeau generalized functions and solvability of differential operators ⋮ Case study of a nonlinear, nonconservative, nonstrictly hyperbolic system ⋮ Maximal closed ideals of the Colombeau algebra of generalized functions ⋮ Symmetric hyperbolic systems in algebras of generalized functions and distributional limits ⋮ Semilinear hyperbolic systems and equations with singular initial data ⋮ Intrinsic definition of the Colombeau algebra of generalized functions ⋮ Wave Equations and Symmetric First-order Systems in Case of Low Regularity ⋮ Delta waves for a strongly singular initial-boundary hyperbolic problem with integral boundary condition ⋮ Semilinear hyperbolic systems with singular non-local boundary conditions: Reflection of singularities and delta waves ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ Associated distributions for a semilinear hyperbolic problem with singular coefficients ⋮ A two-dimensional hyperbolic system of nonlinear conservation laws with functional solutions ⋮ Generalized solutions to partial differential equations of evolution type ⋮ The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory ⋮ Approximations of linear Dirichlet problems with singularities ⋮ A global theory of algebras of generalized functions ⋮ Nonlinear maps in spaces of distributions ⋮ Non-standard shocks in the Buckley-Leverett equation

Cites Work

• Generalized solutions of nonlinear parabolic equations with distributions as initial conditions
• Weak limits of solutions to semilinear hyperbolic systems
• Nonlinear superposition and absorption of delta waves in one space dimension
• A nonlinear theory of generalized functions.
• Generalized solutions to semilinear hyperbolic systems
• On some further properties of solutions to a certain semi-linear system of partial differential equations
• Fourier integral operators. I
• Products of distributions.
• Multiplications of distributions in elasticity and hydrodynamics
• Products of distributions with values in distributions.
• Exact solution of a certain semi-linear system of partial differential equations related toa migrating predation problem

This page was built for publication: On a hyperbolic system with a compatible quadratic