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Interface Problems using the Unified Transform Method

Tuesday, November 29, 2016 - 11:00am - 12:00pm
Lind 305
Natalie Sheils (University of Minnesota, Twin Cities)
Interface problems for partial differential equations are initial boundary value problems for which the solution of an equation in one domain prescribes boundary conditions for the equations in adjacent domains. These types of problems occur widely in applications including heat transfer, quantum mechanics, and mathematical biology. These problems, though linear, are often not solvable analytically using classical approaches. I will present an extension of the Unified Transform Method, alternatively called the Fokas Method, appropriate for solving these types of problems.