Uniqueness of solutions to certain hyperbolic boundary value problems in a semi‐infinite strip

Abstract

It is well known that boundary value problems for hyperbolic equations are in general “not well posed” problems. This paper is concerned with the uniqueness of solutions to boundary value problems for the hyperbolic equation u xx − Qu = u tt . Here Q is a function of the variable x alone, and satisfies the following conditions: (a) Q :[0, ∞) → ℝ; (b) Q is Lebesgue integrable on any compact subinterval of [0, ∞); (c) Q ( x )→ ∞ as x → ∞.