Smooth Solutions of Hyperbolic Equations with Translation by an Arbitrary Vector in the Free Term
Н. В. Зайцева, A. B. Muravnik
Abstract
Abstract We construct three-parameter families of solutions of hyperbolic differential-difference equations in a half-space with a general shift operator in the free term (or in a nonlocal operator potential). It is proved that the solutions obtained are classical if the real part of the symbol of the corresponding differential-difference operators is positive. Classes of equations for which the indicated condition is satisfied are given.
Topics & Concepts
MathematicsHyperbolic partial differential equationTerm (time)Mathematical analysisOperator (biology)Ordinary differential equationPartial differential equationSymbol of a differential operatorDifferential equationPure mathematicsDifferential algebraic equationQuantum mechanicsBiochemistryChemistryGeneRepressorTranscription factorPhysicsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsSpectral Theory in Mathematical Physics