Abstract:
We consider the Cauchy problem with respect to z2 for a homogeneous linear partial differential equation with constant coefficients in two independent variables
z1,z2∈C. We show that the relative smoothness with respect to z1
and z2 of analytic and ultradifferentiable solutions of the Cauchy problem depends essentially on the value of ρ2 and, as a rule, is completely determined by it. We also obtain rather general uniqueness theorems and find conditions which guarantee that the particular solution constructed depends both continuously and linearly on the initial functions.
Citation:
Yu. F. Korobeinik, “Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients”, Izv. Math., 61:3 (1997), 553–592