LOCAL EXISTENCE AND UNIQUENESS THEORY FOR THE SECOND SOUND EQUATION IN ONE SPACE DIMENSION.

We study the local-in-time existence and uniqueness of the Cauchy problem for the nonlinear wave equation $\partial_{t}^2u = u\partial_x(u \partial_x u)$, which is called the second sound equation. Assuming that u(0, x) = φ ≥ A > 0, φ ∈ C1, and ∂xφ ∈ Hs, we establish the uniqueness of solutions without restriction on their amplitude. [ABSTRACT FROM AUTHOR]