Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Author "Ivanova, Nataliya M."
Now showing items 1-9 of 9
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Conservation laws and hierarchies of potential symmetries for certain diffusion equations
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos; Vaneeva, Olena O. (2009)We show that the so-called hidden potential symmetries considered in a recent paper [M.L. Gandarias, New potential symmetries for some evolution equations, Physica A 387 (2008) 2234-2242] are ordinary potential symmetries ...
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Conservation laws and potential symmetries of systems of diffusion equations
Ivanova, Nataliya M.; Sophocleous, Christodoulos (2008)We classify local first-order conservation laws for a class of systems of nonlinear diffusion equations. The derived conservation laws are used to construct the set of inequivalent potential systems for the class under ...
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Group analysis of (2 + 1)- and (3 + 1)-dimensional diffusion-convection equations
Demetriou, Ellie; Ivanova, Nataliya M.; Sophocleous, Christodoulos (2008)We perform the complete Lie group classification of a (2 + 1)- and a (3 + 1)-dimensional classes of non-linear diffusion-convection equations. This classification generalizes and completes existing results in the literature. ...
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Group analysis of variable coefficient diffusion-convection equations. I. Enhanced group classification
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos (2010)We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1 + 1)-dimensional nonlinear ...
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Group classification of a class of equations arising in financial mathematics
Ivanova, Nataliya M.; Sophocleous, Christodoulos; Leach, Peter G. L. (2010)We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven ...
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Article
Lie group analysis of two-dimensional variable-coefficient Burgers equation
Ivanova, Nataliya M.; Sophocleous, Christodoulos; Tracinà, Rita (2010)The modern group analysis of differential equations is used to study a class of two-dimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are ...
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On Degenerations of Algebras over an Arbitrary Field
Ivanova, Nataliya M.; Pallikaros, Christakis A. (2019)We investigate degenerations of $n$-dimensional algebras over an arbitrary infinite field paying particular attention to algebras satisfying the identity $[x,x]=0$ (where $[x_1,x_2]$ denotes the product of the elements ...
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On the group classification of variable-coefficient nonlinear diffusion-convection equations
Ivanova, Nataliya M.; Sophocleous, Christodoulos (2006)We consider the variable coefficient diffusion-convection equation of the form f (x) ut = [g (x) D (u) ux]x + h (x) K (u) ux which has considerable interest in mathematical physics, biology and chemistry. We present a ...
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Similarity reductions of the (1 + 3)-dimensional Burgers equation
Christou, Marios Andreas; Ivanova, Nataliya M.; Sophocleous, Christodoulos (2009)We consider the (1 + 3)-dimensional Burgers equation ut = uxx + uyy + uzz + uux which has considerable interest in mathematical physics. We complete the list of similarity reductions that are obtained from the Lie symmetries ...