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Yuri Bozhkov

Publications and source records attributed to Yuri Bozhkov.

13 recordsLinked to original sources
arXiv2026

Study via Approximate Symmetries of the Emergence of Secondary Flux in the Bevilacqua-Gale\~ao Model

The Bevilacqua-Gale\~ao Model of Anomalous Diffusion introduces two fluxes: a primary flux that follows Fick's law of diffusion, representing the fraction of particles undergoing classical diffusion, and a secondary flux modeled by a fourth-order differential term, which accounts for retention phenomena. We investigate the ``analytic emergence'' of this secondary flux by treating the model as a (singular) perturbation of the heat equation, which describes the classical diffusion. Rather than applying traditional perturbation methods, or a straightforward Fourier transformation, we employ the powerful framework of enhanced modern group analysis to study this problem. Specifically, by utilizing approximate symmetries we derive an analytic expression for the emergent secondary diffusion as a perturbation of the classical diffusion process, the approximate fundamental solution and the approximate solution of the related Cauchy problem.

math.AP↗
arXiv2023

Symmetries of Ricci Flows

In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations -- seen as a "static" Ricci flow -- , and of some particular types of metrics of interest, such as, on warped products of manifolds. Finally, we use the symmetries found to obtain invariant solutions of the Ricci flow for the particular families of metrics considered.

math.DG↗
arXiv2013

Group Classification of a Generalized Black--Scholes--Merton Equation

The complete group classification of a generalization of the Black-Scholes-Merton model is carried out by making use of the underlying equivalence and additional equivalence transformations. For each non linear case obtained through this classification, invariant solutions are given. To that end, two boundary conditions of financial interest are considered, the terminal and the barrier option conditions.

math.AP↗
arXiv2012

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions.

math-ph↗
arXiv2010

Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II

We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.

math.AP↗
arXiv2009

Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on $M$ are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries.

math.AP↗
arXiv2007

Lie Symmetries and Criticality of Semilinear Differential Systems

We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.

math-ph↗
arXiv2005

Noether Symmetries and Critical Exponents

We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.

nlin.SI↗