Roman O Popovych and Nataliya M Ivanova 2004 J. Phys. A: Math. Gen. 37 7547 doi:10.1088/0305-4470/37/30/011
New results on group classification of nonlinear diffusion–convection equations
Roman O Popovych and Nataliya M Ivanova
Show affiliationsUsing 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.
- PACS
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02.30.Hq Ordinary differential equations
- MSC
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60J60 Diffusion processes (See also 58J65)
58J65 Diffusion processes and stochastic analysis on manifolds (See also 35R60, 60H10, 60J60)
- Subjects
- Dates
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Issue 30 (30 July 2004)
Received 7 August 2003, in final form 5 January 2004
Published 14 July 2004
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New results on group classification of nonlinear diffusion–convection equations
Roman O Popovych and Nataliya M Ivanova 2004 J. Phys. A: Math. Gen. 37 7547
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