| Abstract: |
| In this talk we consider initial-boundary value problems (IBVPs) for linear evolution partial differential equations (PDEs) with time-dependent coefficients. We present (for the first time) integral representations of solutions for a big family of these problems; the derivation of these solutions is based on extensions of the unified transform (UT). Based on these solutions we discuss the well-posedness of these IBVPs for certain linear and non-linear PDEs. Finally, we show that, for certain evolution partial PDEs, the solution of IBVPs on a finite interval can be reconstructed as a superposition of solutions to two associated IBVPs posed on the half-line, which provides a completely new perspective on studying this large class of problems. |
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