Auxiliary Lagrangian and Conservation Laws for a Wave Equation Incorporating Dissipation*

Abstract

Abstract In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function. As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013 (2013) 407908]. The results show that our method work for arbitrary functions f(u) and g(u) rather than special ones.