The Existence Of Solutions For A Class Of Nonlinear Parabolic Equations

The parabolic partial differential equtions have many applications in hydrodynam-ics,elasticity and image processing,etc.In recent decades,many scholars have made deep research on parabolic partial differential equations and obtained many interesting results,especially on the p(x)-Laplace equation with nonlinear perturbations.In this paper,we study the p(x)-Laplace equation with nonlinear term in RN.We study the renormalization of the following parabolic p(x)-Laplace equation:(?)where 2 ≤p(x)≤ p+.By using the classical Galerkin approximation and the standard domain expansion technique,we first establish that the p(x)-Laplacian equation has a unique weak solution in RN.Next,by constructing and solving the approxima-tion problem of p(x)-Laplace equation,the renormalized solution of the whole space is obtained.Finally,we prove the existence of a global L1(RN)-attractor for the p(x)-Laplace equation.