Global Holder Continuous Solutions of Nonstrictly Hyperbolic Systems

Abstract

This paper considers the Cauchy problem for nonstrictly hyperbolic systems u_t + \frac{1}{2}(au&sup2 + v&sup2)_x = 0, v_t + (uv)_x = 0 and gives the Hölder continuous solutions under some stronger restrictions of data by applying the method of vanishing viscosity, where a > 2 is a constant.