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math.AP2019
Regular generalized solutions to semilinear wave equations
Hideo Deguchi, Michael Oberguggenberger
The paper is devoted to proving an existence and uniqueness result for generalized solutions to semilinear wave equations with a small nonlinearity in space dimensions 1, 2, 3. The…
math.AP2019
Propagation of singularities for generalized solutions to nonlinear wave equations
Hideo Deguchi, Michael Oberguggenberger
The paper is devoted to regularity theory of generalized solutions to semilinear wave equations with a small nonlinearity. The setting is the one of Colombeau algebras of generaliz…
math.AP2015
Propagation of singularities for generalized solutions to wave equations with discontinuous coefficients
Hideo Deguchi, Michael Oberguggenberger
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau al…