In this series of lectures, we will introduce some basic methods and theories related to parabolic problems. It may include a brief introduction to ODE, local existence and extension, properties of blow-up solutions, global existence, and long-time behavior depending on the interest of the audience and the time. The tentative plan is 4 lectures on Sept 5, 6, 12 and another couple of lectures in Oct. These lectures are accessible to senior undergraduates who have learned Real Analysis; some background in PDE is helpful.
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