Alexey Shevyakov (Alexei Cheviakov) publications page

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Book

Applications of Symmetry Methods to Partial Differential Equations (2010) by G. Bluman, A. F. Cheviakov, and S. C. Anco, Springer: Applied Mathematical Sciences, Vol. 168, ISBN 978-0-387-98612-8.

Papers

• C. Kallendorf, A. F. C, M. Oberlack, and Y. Wang, Conservation laws of surfactant transport equations. Physics of Fluids 24, 102105 (2012). [PDF]
• A. F. C,  J.-F. Ganghoffer, Symmetry properties of two-dimensional Ciarlet–Mooney–Rivlin constitutive models in nonlinear elastodynamics. J. Math. Anal. Appl. 396 (2012) 625–639 [PDF]
• A.S. Reimer, A. F. C., A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet–Neumann boundary conditions. Computer Physics Communications ??? (2012) [PDF]
• A. F. C., A.S. Reimer, M. J. Ward, Mathematical Modeling and Numerical Computation of Narrow Escape Problems. Physical Rev. E 85, 021131 (2012) [PDF]
• A. F. C., Symbolic Computation of Local Symmetries of Nonlinear and Linear Partial and Ordinary Differential Equations. Math.Comput.Sci. (2010) 4:203–222 [PDF]
• A. F. C. and G. W. Bluman, Multi-dimensional PDE Systems: Generating New Systems Via Conservation Laws, Potentials, Gauges, Subsystems. J. Math. Phys. 51, (2010), 103521 [PDF]
• A. F. C. and G. W. Bluman, Multi-dimensional PDE Systems: Nonlocal Symmetries, Nonlocal Conservation Laws, Exact Solutions. J. Math. Phys. 51, (2010), 103522 [PDF]
• A. F. C. and G. W. Bluman, On locally and nonlocally related potential systems. J. Math. Phys. 51, (2010), 073502 [PDF]
• A. F. C., M. J. Ward, and R. Straube, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere.  SIAM Multiscale Modeling and Simulation, 2010 [PDF]
• A. F. C. and M. J. Ward, Optimizing the Principal Eigenvalue of the Laplacian in a Sphere with Interior Traps. Mathematical and Computer Modelling, 2010 [PDF]
• M. Oberlack and A. F. C., Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes, J. Eng. Math. (2009). [PDF]
• G. W. Bluman, A. F. C., and J.-F. Ganghoffer, On the nonlocal symmetries, group invariant solutions and conservation laws of the equations of nonlinear dynamical compressible elasticity, Accepted to Proc.
  IUTAM (2009). [PDF]
• A. F. C. and J. Hartwick, Constant Per Capita Consumption Paths with Exhaustible Resources and Decaying Produced Capital, Accepted to Ecological Economics (2009). [PDF]
• A. F. C., Computation of fluxes of conservation laws, J. Eng. Math. (2009), DOI: 10.1007/s10665-009-9307-x [PDF]
• G. W. Bluman, A. F. C., and S. C. Anco, Construction of Conservation Laws: How the Direct Method Generalizes Noether's Theorem, Proc. 4th Workshop ``Group Analysis of Differential Equations &
  Integrability'' (2009), 1-23. [PDF]
• A. F. C., An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics, J. Math. Phys. 49, (2008), 083502  [PDF]
• G. Bluman, A. F. C., and J.-F. Ganghoffer, Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics, J. Eng. Math., online DOI 10.1007/s10665-008-9221-7 (2008). [PDF]
• G. Bluman, A. F. C., and M. Senthilvelan, Solution andAsymptotic/Blow-up Behaviour of a Class of Nonlinear Dissipative Systems, J. Math. An. App. 339 (2008), 1199--1209. [PDF]
• A. F. C. and S. C. Anco, Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions, Phys. Lett. A 372 (2008) 1363--1373. [PDF]
• A. F. C. and M. J. Ward, A Two--Dimensional Metastable Flame-Front and a Degenerate Spike--Layer Problem, Interfaces and Free Boundaries 9 (2007), 513--547. [PDF]
• G. Bluman and A. F. C., Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation, J. Math. An. App. 333 (2007), 93--111. [PDF]
• A. F. C., “GeM software package for computation of symmetries and conservation laws of differential equations”. Comp. Phys. Comm. 176 (2007) 48–-61  [PDF]
• G. Bluman , A. F. C., and N. M. Ivanona, “Framework for nonlocally related PDE systems: simplification; new symmetries and conservation laws for NLT equations,” J. Math. Phys. 47 (2006), 113505. [PDF]
• G. Bluman  and A. F. C. “Framework for potential systems and nonlocal symmetries: Algorithmic approach,” J. Math. Phys. 46, 123506 (2005) [PDF]
• A. F. C. “Construction of exact plasma equilibrium solutions with different geometries,” Phys. Rev. Lett. 94, 165001 (2005) [PDF]
• A. F. C. and J. Hartwick  "Beckmann's Edgeworth-Bertrand Duopoly Example Revisited." Int. Game Theory Rev. 7 (4), 461-471 (2005) .
• A. F. C. “Analytical 3-Dimensional Anisotropic Magnetohydrodynamic Equilibria.” Topology and its Applications 152, 157–173 (2005).
• A. F. C. “Exact plasma equilibria from symmetries and transformations of MHD and CGL equilibrium equations,” in: “Symmetry Methods in Physics” (ed. C.Burdik, O.Navratil, S.Posta), Prague, Czech Rep., ISBN 5-9530-0069-3 (2004) [PDF]
• A. F. C. and O. I. Bogoyavlenskij  “Exact anisotropic MHD equilibria”, J. Phys. A 37, 7593 – 7607 (2004) [PDF]
• A. F. C. “Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations,” Phys. Lett. A 321, 34-49 (2004) [PDF]
• A. F. C. “Bogoyavlenskij symmetries of isotropic and anisotropic MHD equilibria are Lie point transformations”, Proc. Inst. Math. NAS Ukraine, 50, 69-76 (2004) [PDF]
• N. A. Kudryashov, G. S.  Romanov, and A. F. C., “Numerical simulation of the quasistationary phase of a volcanic eruption in the initial stage”, Engineering-Physics Journal (Russian) / JEPTER (English) 76, 795-803 (2003) [PDF]
• N. A. Kudryashov, G. S.  Romanov and A. F. C. “Numerical modeling of explosive volcanic eruptions”, Eng.-Phys. J. (Rus) / JEPTER (Eng). 75, 521-528 (2002).
• N. A. Kudryashov and A. F. C. “Self-Similar Solutions of 1-Dimentional Problems of Gas Filtration with Square Law of Resistance,” Eng.-Phys. J. (Rus) / JEPTER (Eng). 72, 1090-1099 (1999).

Ph.D. thesis

• "SYMMETRIES AND EXACT SOLUTIONS OF PLASMA EQUILIBRIUM EQUATIONS" [PDF] 
      Queen's University at Kingston, 2004.
      Supervisor: Prof. O.I.Bogoyavlenskij

Some posters

• "Exact Solutions of Ideal Plasma Equilibria" (2011) [PDF],
          with Stephanie Goertzen, UofS USTEP summer undergraduate student.
• "Optimal Arrangements and Homogenization Limit for Traps on the Sphere" (2011) [PDF],
          with Daniel Zawada, NSERC USRA summer undergraduate student.
• "Mathematical Modelling of Narrow Escape Problems" (2010) [PDF],
          with Ashton Reimer, NSERC USRA summer undergraduate student.

Recent talks

• "Symmetry Methods for Differential Equations and Their Applications in Mathematical Modeling", Math Colloquium, University of Regina, Jan. 20, 2012 [PDF]
• "Conservation Laws: Systematic Construction, Noether's Theorem, Applications, and Symbolic Computations", Physics Seminar, UofS, Nov.10, 2011 [PDF]
• "A Maple-based Package for Computation of Conservation Laws, Symmetries and Invariant forms of DEs", ICIAM 2011, Vancouver [PDF]
• "Direct Method of Construction of Conservation Laws for Nonlinear Differential Equations, its Relation with Noether's Theorem, Applications, and Symbolic Software", INPL seminar, Nancy, France, 2011 [PDF]
• "Mathematical Modeling, Numerical Computation, and Applications of Narrow Escape Problems", PRNMS 2011, Regina [PDF]
• Session: "Symmetry Methods for Differential Equations", CMS-2010 winter meeting, Dec.3-5, 2010. Vancouver, BC, Canada [Talks]
• "An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems for the Sphere", Optimal Configurations on the Sphere and Other Manifolds, Vanderbilt University, 2010. [PDF]
• "Narrow Escape Problems: Asymptotic Optimization of Locations of Small Traps for the Unit Sphere", CMS-2009 winter meeting, [PDF]
• "An extended procedure for finding exact solutions of PDEs arising from potential symmetries", Symmetry in Nonlinear Mathematical Physics, Kiev, 2009 [PDF]
• "Computation and applications of local conservation laws", PNRMS, University of Saskatchewan, 2009 [PDF]
• "Nonlocally Related PDE Systems", TU Darmstadt, May 2008 [PDF]
• "Computation of Conservation Laws Admitted by PDEs", TU Darmstadt, May 2008 [PDF]
• "Computation of Point Symmetries Admitted by DEs", TU Darmstadt, May 2008 [PDF]
• "Modern Symmetry Methods for PDEs. Applications to Mathematical Modeling and Analysis". UofS, 2008. [PDF]

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