Vol. 22, No. 2, 1967

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On the behavior of the solution of the telegraphist’s equation for large velocities

Larry Eugene Bobisud

Vol. 22 (1967), No. 2, 213–219
Abstract

Consider the solution φ of the inhomogeneous telegraphist’s equation with signal velocity 1√ 𝜖,- where φ satisfies the initial conditions φ(x,0) = g(x)t(x,0) = h(x). Let U be the solution of the parabolic equation that results from the telegraphist’s equation when the velocity is set equal to (𝜖 = 0), and let U satisfy the initial condition U(i1i,0) = g(x). Our main result is that, under suitable conditions on the coefficients and data,

∫
∞                2      √-
− ∞[φ(x,t) − U (x,t)]dx = 0( 𝜖)

uniformly in 0 t t for any finite t.

Mathematical Subject Classification
Primary: 35.79
Milestones
Received: 5 May 1966
Published: 1 August 1967
Authors
Larry Eugene Bobisud