On a nonlocal singular mixed evolution problem

Abstract

In the present paper, the existence and uniqueness of the strong solution of a mixed problem for a second order plurihyperbolic equation with an integral condition is proved. The proof is essentially based on an a priori bound and on the density of the range of the operator generated by the considered problem. In spite of the apparant simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these technics to the considered equation in more than one dimension without imposing complementary conditions.