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

Author:

Torrisi Mariano1ORCID,Tracinà Rita1ORCID

Affiliation:

1. Dipartimento di Matematica e Informatica, Università Degli Studi di Catania, Viale Andrea Doria, 6, 95125 Catania, Italy

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.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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