The nonlinear boundary value problem with a p(x)-Laplace type operator under Dirichlet boundary condition is studied. The condition of regularity is relaxed on the variable exponent p(⋅) and on the function b appearing in the governing equation. Although the existence and uniqueness of weak energy solution presented in Section 3 is trivial, an attempt has been made to develop the existence and uniqueness of the entropy solution of the problem.

generalized Lebesgue-Sobolev spaces; weak energy solution; entropy production; p(x)-Laplace operator