BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:S. V. Meleshko (Suranaree University of Technology\, Nakhon Ratcha sima\, Thailand) DTSTART:20250320T110000Z DTEND:20250320T120000Z DTSTAMP:20260423T024022Z UID:mmandim/90 DESCRIPTION:Title: Equivalence to the classical heat equation through reciprocal transformat ions\nby S. V. Meleshko (Suranaree University of Technology\, Nakhon R atchasima\, Thailand) as part of Mathematical models and integration metho ds\n\n\nAbstract\nThis paper investigates the equivalence of parabolic par tial differential equations to the classical\none-dimensional heat equatio n using reciprocal transformations. The equations are assumed to be autono mous\, and the methodology applied is similar to S. Lie’s approach to so lving the linearization problem of second-order ordinary differential equa tions. The research is structured in two main parts. In the first part\, n ecessary constraints on the class of parabolic partial differential equati ons with two independent variables\, which are equivalent to the classical heat equation under a reciprocal transformation\, are identified. In the second part\, the remaining conditions are examined\, and sufficient condi tions are derived. The corresponding differential equations are then obtai ned. All possible cases that arise are thoroughly analyzed\, and the theor y is illustrated with several examples.\n\nThis is joint work with P. Siri wat (Thailand) and S. R. Svirshchevskii (Russia).\n LOCATION:https://researchseminars.org/talk/mmandim/90/ END:VEVENT END:VCALENDAR