Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents

The first boundary value problem is considered for a certain class of anisotropic parabolic equations with variable nonlinearity exponents in a cylindrical domain , where is a bounded domain. The parabolic term in the equation has the form and is determined by the function , where , which only satisfies the Carathéodory condition and is increasing in . The existence of a weak and a renormalized solution is proved. Bibliography: 26 titles.