The Cauchy problem (constant coefficients)

Abstract

To solve the Cauchy problem for a differential operator P (D) with data on a plane 〈x,N〉 = 0, where 0≠N∈R _n , means, roughly speaking, to find a solution u of the equation

$$P(D)u=f,$$

(5.0.1)

where f is given, so that for another given function φ

$$u-\varphi =O({{\left\langle x,N \right\rangle }^{m}})when\left\langle x,N \right\rangle \to 0.$$

(5.0.2)