Geodesic
On global classical solutions of hyperbolic differential-difference equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 44-46

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A one-parameter family of global solutions of a two-dimensional hyperbolic differential-difference equation with an operator acting with respect to a space variable is constructed. A theorem is proved stating that the resulting solutions are classical for all parameter values if the symbol of the difference operator of the equation has a positive real part. Classes of equations for which this condition is satisfied are given.
Keywords: hyperbolic equation, differential-difference equation, classical solution, Fourier transform. 
@article{DANMA_2020_491_a7,
     author = {N. V. Zaitseva},
     title = {On global classical solutions of hyperbolic differential-difference equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {44--46},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a7/}
}
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N. V. Zaitseva. On global classical solutions of hyperbolic differential-difference equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 44-46. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a7/