A pointwise oscillation property of semilinear wave equations with time-dependent coefficients Original Research Article

We shall consider a one-dimensional semilinear wave equation in a finite interval (0,l) in View the MathML source. A usual homogeneous boundary condition is imposed on it at x=0,l. We shall show that the solution u(x,t) oscillates on the time t in the following sense. Let x be any fixed in (0,l), then u(x,t) changes its sign infinitely many times as t is passing.