Classical Solutions of Hyperbolic Differential-Difference Equations with Differently Directed Translations
A. B. Muravnik, Н. В. Зайцева
Abstract
Abstract In the half-space, three-parameter families of solutions are constructed for hyperbolic differential-difference equations with general-type translation operators acting with respect to all spatial variables. We prove that the obtained solutions are classical provided that the real part of the symbol of the corresponding differential-difference operator is positive. Classes of equations such that this condition is satisfied for them are provided.
Topics & Concepts
MathematicsHyperbolic partial differential equationMathematical analysisDifferential equationOperator (biology)Type (biology)Space (punctuation)Pure mathematicsPhilosophyTranscription factorGeneLinguisticsChemistryRepressorBiologyEcologyBiochemistryDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering