A non‐linear hyperbolic equation

Abstract

In this paper the following Cauchy problem, in a Hilbert space H , is considered: urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0001 urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0002 urn:x-wiley:01611712:media:ijmm732105:ijmm732105-math-0003 M and f are given functions, A an operator in H , satisfying convenient hypothesis, λ ≥ 0 and α is a real number. For u 0 in the domain of A and u 1 in the domain of , if λ > 0, and u 1 in H , when λ = 0, a theorem of existence and uniqueness of weak solution is proved.