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|Doctoral Committee Chair(s):||Jerrard, Robert L.|
|Department / Program:||Mathematics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||We present an axiomatic approach to certain geometric evolution problems and associated level set PDEs. We also study threshold dynamics on Rn and cellular automata on certain lattices which satisfy monotonicity, translation invariance and finite propagation speed. We develop the general schemes for the convergence of threshold dynamics and cellular automata to geometric evolutions governed by a velocity function depending on the normal direction alone.|
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
|Date Available in IDEALS:||2015-09-28|