Well-posed problems in algebras of generalized functions

DOI10.1080/00036811.2010.511474zbMath1235.35009OpenAlexW1986914560WikidataQ58159404 ScholiaQ58159404MaRDI QIDQ3096912

Victor Dévoué, Antoine Delcroix, Jean-André Marti

Publication date: 15 November 2011

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2010.511474

zbMATH Keywords

non-Lipschitz nonlinearitynonlinear generalized functionsregularization of dataregularization of problemscharacteristic nonlinear Cauchy problemdistribution as initial data

Mathematics Subject Classification ID

Distributions and generalized functions on nonlinear spaces (46T30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Other special methods applied to PDEs (35A25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (4)

Study of nonlinear stochastic Cauchy problems in $(\mathcal{C},\mathcal{E},\mathcal{P})$-algebras ⋮ Generalized solution to a non Lipschitz integral equation ⋮ Some nonlinear stochastic Cauchy problems with generalized stochastic processes ⋮ Solving a hyperbolic equation in the first canonical form

Cites Work

• Divergent type quasilinear Dirichlet problem with singularities
• Generalized solutions of singular differential problems. Relationship with classical solutions
• Nonlinear algebraic analysis of delta shock wave solutions to Burgers' equation.
• Topology on asymptotic algebras of generalized functions and applications
• Topology and functoriality in \((\mathcal {C, E, P})\)-algebras. Application to singular differential problems
• A new approach to temperate generalized Colombeau functions
• Comparison of some solution concepts for linear first-order hyperbolic differential equations with non-smooth coefficients
• A nonlinear goursat problem with irregular data
• A Multivariate Faa di Bruno Formula with Applications

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