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

Larry Eugene Bobisud

Vol. 22 (1967), No. 2, 213–219

DOI: 10.2140/pjm.1967.22.213

Abstract

Consider the solution φ of the inhomogeneous telegraphist’s equation with signal velocity 1∕ where φ satisfies the initial conditions φ(x,0) = g(x),φ_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,

uniformly in 0 ≦ t ≦t for any finite t.

Mathematical Subject Classification

Primary: 35.79

Milestones

Received: 5 May 1966

Published: 1 August 1967