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One-dimensional adhesion model for large scale structures. (English) Zbl 1189.35174

Summary: We discuss initial value problems and initial boundary value problems for some systems of partial differential equations appearing in the modelling for the large scale structure formation in the universe. We restrict the initial data to be bounded measurable and locally bounded variation function and use Volpert product to justify the product which appear in the equation. For more general initial data in the class of generalized functions of Colombeau, we construct the solution in the sense of association.

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35A20 Analyticity in context of PDEs
35R05 PDEs with low regular coefficients and/or low regular data
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
35L45 Initial value problems for first-order hyperbolic systems
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