Decay of entropy solutions of nonlinear conservation laws (Q1300697)

The authors study the large time behaviour of periodic entropy solutions to the Cauchy problem for hyperbolic systems of conservation laws \[ u_t+\nabla_x\cdot f(u)=0, \quad u\in{\mathbb R}^m, \quad x\in{\mathbb R}^n,\qquad u(x,0)=u_0(x). \] The general approach is introduced mainly based on scale-invariance of the equations and compactness of the solution operator (under appropriate nondegeneracy conditions). The authors apply this approach to prove decay properties of \(L^\infty\) periodic entropy solutions for multidimensional scalar conservation laws and for some important hyperbolic systems of conservation laws. Conservation laws with relaxation are considered as well.