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SUMMARY:S. A. Rukolaine (Ioffe Institute\, St. Petersburg\, Russia)
DTSTART:20260507T110000Z
DTEND:20260507T120000Z
DTSTAMP:20260603T003615Z
UID:mmandim/113
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/113/
 ">The Fokas unified transform method</a>\nby S. A. Rukolaine (Ioffe Instit
 ute\, St. Petersburg\, Russia) as part of Mathematical models and integrat
 ion methods\n\n\nAbstract\nThe method was developed to solve initial-bound
 ary value problems for integrable nonlinear partial differential equations
  (PDEs) having a Lax pair. It turned out that the method also provides a u
 nified algorithmic approach to solving initial-boundary and boundary value
  problems for linear PDEs. At the same time\, the Fokas method allows solv
 ing problems that cannot be solved by the Fourier method.\n\nIn the talk\,
  we describe the Fokas method as applied to solving initial-boundary value
  problems for linear evolutionary PDEs. We show how the Fokas method is us
 ed to solve initial-boundary value problems for a pseudoparabolic PDE and 
 systems of linear PDEs\, see [1-4]. In the final part of the talk\, the Fo
 kas method is demonstrated in its most general form (using the Lax pair\, 
 reducing to the Riemann-Hilbert problem)\, which is applicable to both lin
 ear and nonlinear PDEs.\n\nReferences:\n\n1. S. A. Rukolaine\, Integral Re
 presentation of Solutions to Initial-Boundary Value Problems on a Finite I
 nterval in the Framework of the Hyperbolic Heat Equation\, Math. Meth. App
 l. Sci.\, 48:13760-13772\, 2025. https://doi.org/10.1002/mma.11140\n\n2. S
 . A. Rukolaine\, Analytical representation of heat waves on a finite inter
 val in the framework of the hyperbolic heat equation. Proceedings of the I
 nternational Conference ``Days on Diffraction 2025''\, St. Petersburg\, Ru
 ssia\, June 16-20\, 2025\, pp. 181-187. https://doi.org/10.1109/DD66835.20
 25.11263496\n\n3. A. Chatziafratis\, S. A. Rukolaine\, E. C. Aifantis\, In
 tegral representations for the Barenblatt-Sobolev-Galpern pseudo-parabolic
  equation: boundary-value and interface problems on unbounded and finite i
 ntervals\, Russ. J. Math. Phys.\, 2026. (Accepted)\n\n4. S. A. Rukolaine\,
  The Guyer-Krumhansl model of heat conduction on a finite interval. (Submi
 tted) https://arxiv.org/abs/2502.20057v2\n
LOCATION:https://researchseminars.org/talk/mmandim/113/
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