On the solutions of some classes of PDE with singular coefficients

ABSTRACT

We consider the linear Cauchy problem with analytic data for two models of second order operators with singular coefficients. We show that the propagation of the singularities of the coefficients of the subprincipal part of the operators generate singularities on the union of the characteristic surfaces, on the surfaces $x_1=0$, $x_2=0$ and on the characteristic cone too.

KEYWORDS:

• Cauchy problem
• Appell's function $F_3$
• singular coefficients
• singular solutions

AMS SUBJECT CLASSIFICATIONS:

• 35Q05
• 33C65
• 35A20
• 35C05
• 35C10

Acknowledgments

The author thanks the referee for his nice comments about the paper.

Disclosure statement

No potential conflict of interest was reported by the author.