S. Kovalenko

most citedLie symmetry properties of nonlinear reaction-diffusion equations with gradient-dependent diffusivity

39 citations · 55 across the 2 of their papers we have counts for

collaborators

2 papers

q-fin.MF2015★ 16 cited

Symmetry reduction and exact solutions of the non-linear Black--Scholes equation

Oleksii Patsiuk, Sergii Kovalenko

In this paper, we investigate the non-linear Black--Scholes equation: $u_{t} + a x^{2} u_{xx} + b x^{3} u_{xx}^{2} + c (x u_{x} - u) = 0, a, b > 0, c \geq 0.$ and show that the one can be reduced to the…

math-ph2015★ 39 cited

Lie symmetry properties of nonlinear reaction-diffusion equations with gradient-dependent diffusivity

R. Cherniha, J. R. King, S. Kovalenko

Complete descriptions of the Lie symmetries of a class of nonlinear reaction-diffusion equations with gradient-dependent diffusivity in one and two space dimensions are obtained. A…