Vol. 85, No. 2, 1979

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ISSN: 0030-8730
On the characterizations of the breakdown points of quasilinear wave equations

Peter H. Chang

Vol. 85 (1979), No. 2, 361–381
Abstract

We consider the mixed initial and boundary value problem of the quasilinear wave equation:

     ut − vx = 0,
v − Q2 (u)u  = 0;
t        x
(1)

u(x,0) = 0, v(x,0) = v0(x),  0 ≦ x ≦ 1,
v(0,t) = v(1,t) = 0, t ≧ 0.
(2)

In general the solution of the system (1), (2) eventually breaks down in the sense that some of its flrst derivatives become unbounded at a finite time. It is shown that there are only finitely many breakdown points and that at each of them there originates one or two shock curves.

Mathematical Subject Classification 2000
Primary: 35L65
Secondary: 76L05
Milestones
Received: 21 November 1977
Revised: 29 December 1978
Published: 1 December 1979
Authors
Peter H. Chang