High Frequency Waves and the Maximal Smoothing Effect for Nonlinear Scalar Conservation Laws
High Frequency Waves and the Maximal Smoothing Effect for Nonlinear Scalar Conservation Laws
The article first studies the propagation of well prepared high frequency waves with small amplitude $\varepsilon$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, and Tadmor [J. Amer. Math. Soc., 7 (1994), pp. …