Vol. 19, No. 1, 1966

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Maximum and monotonicity properties of initial boundary value problems for hyperbolic equations

Duane Sather

Vol. 19 (1966), No. 1, 141–157

Various maximum and monotonicity properties of some initial boundary value problems for classes of linear second order hyperbolic partial differential operators in two independent variables are established. For example, let M be such an operator in Cartesian coordinates (x,y) and let T be a domain bounded by a characteristic curve of M with everywhere negative slope, and segments OA and OB of the positive x-axis and the positive y-axis, respectively; under certain restrictions on the coefficients of the operator M, if Mu 0 in T, u = 0 on OA OB and ∂u∕∂y 0 on OA then u(x,y) 0 in T.

Such maximum and monotonicity properties also have applications to ordinary differential equations; the above mentioned maximum property yields a comparison theorem on the distance between zeros of solutions to some ordinary differential equations.

Mathematical Subject Classification
Primary: 35.55
Received: 21 July 1965
Published: 1 October 1966
Duane Sather