Generalized Solutions to a Non Lipschitz-Cauchy Problem

DOI10.1515/JAA.2009.1zbMath1180.35165OpenAlexW2128833876MaRDI QIDQ3399033

Victor Dévoué

Publication date: 29 September 2009

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jaa.2009.1

zbMATH Keywords

characteristic Cauchy problemnon Lipschitz nonlinearitythree parameter family of problems

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Generalized solutions to partial differential equations (35D99) Second-order semilinear hyperbolic equations (35L71)

Related Items (6)

Study of nonlinear stochastic Cauchy problems in $(\mathcal{C},\mathcal{E},\mathcal{P})$-algebras ⋮ On the Well-posedness of Some generalized Characteristic Cauchy Problems ⋮ Generalized solution to a non Lipschitz integral equation ⋮ Some nonlinear stochastic Cauchy problems with generalized stochastic processes ⋮ Topology and functoriality in \((\mathcal {C, E, P})\)-algebras. Application to singular differential problems ⋮ Solving a hyperbolic equation in the first canonical form

Cites Work

• Generalized solutions to a semilinear wave equation
• Nonlinear algebraic analysis of delta shock wave solutions to Burgers' equation.
• Topology on asymptotic algebras of generalized functions and applications
• On generalized solutions to the wave equation in canonical form
• Fundamental structures and asymptotic microlocalization in sheaves of generalized functions
• A nonlinear goursat problem with irregular data
• A Multivariate Faa di Bruno Formula with Applications

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