Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and \(L^{1}\) data (Q2379271)

The Cauchy problem for the evolutionary \(p(x)\)-Laplacian equation with a variable exponent \(p(x)\) is considered in a bounded domain. The right-hand side of the equation (a source term) is a function \(f\in L^1\). The existence and uniqueness of renormalized solutions is obtain. The same result is proved for entropy solutions. It follows that both classes of solutions are equivalent.