Abstract: | We study the p-system with viscosity given by vt ? ux = 0, ut + p(v)x = (k(v)ux)x + f(∫ vdx, t), with the initial and the boundary conditions (v(x, 0), u(x,0)) = (v0, u0(x)), u(0,t) = u(X,t) = 0. To describe the motion of the fluid more realistically, many equations of state, namely the function p(v) have been proposed. In this paper, we adopt Planck's equation, which is defined only for v > b(> 0) and not a monotonic function of v, and prove the global existence of the smooth solution. The essential point of the proof is to obtain the bound of v of the form b < h(T) ? v(x, t) ? H(T) < ∞ for some constants h(T) and H(T). |