Multiplication of distributions

DOI10.1090/S0273-0979-1990-15919-1zbMath0731.46023MaRDI QIDQ5896579

J. François Colombeau

Publication date: 1990

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

boundary conditionssystems of partial differential equationsmultiplication of distributionsCobombeau algebrasolutions of algebraic differential equations

Mathematics Subject Classification ID

Related Items (51)

Stochastic boundary value problems: A white noise functional approach ⋮ Nonlinear generalized sections of vector bundles ⋮ Measurements of ordinary and stochastic differential equations. ⋮ Microlocal analysis of Colombeau's generalized functions on a manifold ⋮ Up to \(\varepsilon\) methods for systems modeling permanent gases. ⋮ Scattering of classical and quantum particles by impulsive fields ⋮ Generalized solutions to a Cauchy problem for a nonconservative hyperbolic system ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ A relativistic variant of the Wigner function ⋮ Loop calculations in quantum mechanical nonlinear sigma models with fermions and applications to anomalies ⋮ Entropy jump across an inviscid shock wave ⋮ On the quantization of continuous non-ultralocal integrable systems ⋮ A new algebra of periodic generalized functions ⋮ Stability properties of stochastic partial differential equations ⋮ Generalized and classical solutions of nonlinear parabolic equations ⋮ Wave equation driven by fractional generalized stochastic processes ⋮ Division problem and partial differential equations with constant coefficients in Colombeau's space of new generalized functions ⋮ The classical theory of calculus of variations for generalized functions ⋮ On the numerical solution of nonconservative hyperbolic systems of equations ⋮ Interpolating between asymptotic and near horizon symmetries ⋮ Calculus in the ring of Fermat reals. I: Integral calculus ⋮ Screw and edge dislocations with time-dependent core width: from dynamical core equations to an equation of motion ⋮ Numerical verification of delta shock waves for pressureless gas dynamics ⋮ Nonlinear generalized functions and jump conditions for a standard one pressure liquid-gas model ⋮ Intrinsic definition of the Colombeau algebra of generalized functions ⋮ Generalized Solutions of a Periodic Goursat Problem ⋮ Generalized solutions of the multidimensional stochastic Burgers equation ⋮ Linear equations with singular coefficients and nonlinear equations with non-lipschitz nonlinearities ⋮ Semilinear geometric optics for generalized solutions ⋮ Conservation laws with discontinuous coefficients ⋮ Riemann curvature of a boosted spacetime geometry ⋮ Microlocal properties of basic operations in Colombeau algebras ⋮ Entropy preserving low dissipative shock capturing with wave-characteristic based sensor for high-order methods ⋮ Approximate generalized solutions and measure-valued solutions to conservation laws ⋮ On Ruelle's construction of the thermodynamic limit for the classical microcanonical entropy ⋮ Bound and scattering states for supersingular potentials ⋮ Generalized solutions to partial differential equations of evolution type ⋮ Invariance of Unruh and Hawking radiation under matter-induced supertranslations ⋮ Distributional geometry in general relativity ⋮ Stability of stationary solutions of singular systems of balance laws ⋮ The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory ⋮ Nonlinear parabolic equations with regularized derivatives ⋮ Burgers equation with a passive scalar: Dissipation anomaly and Colombeau calculus ⋮ Scalar products of elementary distributions ⋮ The classical point electron in Colombeau’s theory of nonlinear generalized functions ⋮ Locally convex topological algebras of generalized functions: Compactness and nuclearity in a nonlinear context ⋮ COHERENT CHAOS INTEREST-RATE MODELS ⋮ A global theory of algebras of generalized functions ⋮ Nonlinear maps in spaces of distributions ⋮ Some approximate Godunov schemes to compute shallow-water equations with topography. ⋮ The \(\gamma\) function in quantum theory. II: Mathematical challenges and paradoxa

Cites Work

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• Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations
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• Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics
• A multiplication of distributions
• Generalized solutions of algebraic differential equations
• Solutions of algebraic differential equations
• A nonlinear theory of generalized functions.
• Generalized solutions to semilinear hyperbolic systems
• Measure-valued solutions to conservation laws
• Some Research Problems about Algebraic Differential Equations
• The elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions
• Products of distributions.
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• Microscopic Profiles of Shock Waves and Ambiguities in Multiplications of Distributions

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