New results on group classification of nonlinear diffusion–convection equations

By R. Popovych, N. M. Ivanova. 2003

154 citations recorded by the source corpus.

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient (1 + 1)-dimensional nonlinear diffusion?convection equations of the general form f(x)ut = (D(u)ux)x + K(u)ux. We obtain new interesting cases of such equations with the density f localized in space, which have non-trivial invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.

Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/459097ec39208cfed630a0f87eeacab9cda817b1

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In Geometry and Topology

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Lie symmetries and form-preserving transformations of reaction-diffusion-convection equations (2008, methodology): “It should be noted that form-preserving transformations were applied to derive the complete Lie symmetry classification of classes of diffusion–convection and reaction–diffusion equations with variable (with respect to the independent variable x) coefficients in the recent papers [10,23].”
On the group classification of variable-coefficient nonlinear diffusion-convection equations (2006, methodology): “(For more details about the method see [34] and references therein.”