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Alexander, Stephanie B. Bishop, Richard L. Alexander, Stephanie B. Ghrist, Robert Berg, I. David Kapovitch, Ilia Leininger, Christopher J. Jun, Chanyoung 2012-05-22T00:27:23Z 2012-05-22T00:27:23Z 2012-05 2012-05-22T00:27:23Z 2012-05 In this dissertation, we consider an applied problem, namely, pursuit-evasion games. These problems are related to robotics, control theory and computer simulations. We want to find the solution curves of differential equations for pursuit-evasion games, and investigate the properties of solution curves. First, we define CAT(0) and CAT(K) spaces, and explain why they are suitable playing fields, that vastly generalize the usual playing field in the pursuit-evasion literature. Then we prove our existence and uniqueness theorems for continuous pursuit curves in CAT(K) spaces, as well as our convergence estimates and regularity theorem. Pursuit curves are downward gradient curves for the distance from a moving evader, that is, for a time-dependent gradient flow. We consider not only pursuit curves, but also more general time-dependent gradient flow. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-10T13:58:23Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 JUN_CHANYOUNG.zip: 524915 bytes, checksum: e722290ffe2a5c0ac0f329d6439f61cb (MD5) JUN_CHANYOUNG.pdf: 283237 bytes, checksum: 746df7ed91c9f73a2ea86729d2ff7d8e (MD5) Made available in DSpace on 2012-05-22T00:27:23Z (GMT). No. of bitstreams: 3 JUN_CHANYOUNG.pdf: 283237 bytes, checksum: 746df7ed91c9f73a2ea86729d2ff7d8e (MD5) JUN_CHANYOUNG.zip: 524915 bytes, checksum: e722290ffe2a5c0ac0f329d6439f61cb (MD5) license.txt: 4060 bytes, checksum: 57bc5119d18e4101bb3bb553549b366d (MD5) http://hdl.handle.net/2142/31092 en Copyright 2012 Chanyoung Jun CAT(K) spaces Time-dependent gradient curves Pursuit-evasion and time-dependent gradient flow in singular spaces text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD