Symmetries and Conservation Laws for a Class of Fourth-Order Reaction–Diffusion–Advection Equations

Abstract

We have studied a class of (1+1)-dimensional equations that models phenomena with heterogeneous diffusion, advection, and reaction. We have analyzed these fourth-order partial differential equations within the framework of group methods. In this class, the diffusion coefficient is constant, while the coefficients of advection and the reaction term are assumed to depend on the unknown density u(t,x). We have identified the Lie symmetries extending the Principal Algebra along with all the conservation laws corresponding to the different forms of the coefficients, and have derived several brief applications.

Keywords

• heterogenous diffusion
• advection–reaction equations
• Lie symmetries
• conservation laws
• first integrals
• exact solutions