Geometric measure theory and hyperbolic operators ant its numerical calculations

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In this research work, hyperbolic free boundary problems have been treated. The basic equation expresses a model for peeling off a tape from a plane. Based on this model, we established a new method analyzing bubble motion on water surface or small droplet motion with dynamic contact angle on obstacle. In the case of everal attached bubbles, we developed an efficient algorithm which can automatically deal with moving junctions including topological changes. On the ther hand, we have constructed a numerical solver for the problem of bouncing elastic shell via the discrete Morse flow method. Using this algorithm, we are able to incorporate inner structure and analyze the interactionbetween the shell and its contents.