Global and blowup solutions for quasilinear parabolic equations and their numerical computations

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Quasilinear degenerate parabolic equations have many applications in Physics, Chemistry, Biology and image processing. These equations involve a degenerate or singular diffusion term and some kinds of blowup properties which create many challenging problems in global, blowup and numerical solutions. The objectives of this research program involve using a new functional method and moving mesh methods to investigate the properties of global and blowup solutions both theoretically and numerically. The expected results will include the following: