Existence and uniqueness of solutions to the GRID macroscopic growth equation |
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| Authors: | N Portman ER Vrscay |
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| Institution: | Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
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| Abstract: | In this paper we prove the existence and uniqueness of solutions to the initial value problems associated with the GRID integro-differential equation describing macroscopic growth of an organism. We consider the general form of the macroscopic growth operator Φ and study the set of conditions on Φ that are sufficient to guarantee existence and uniqueness of solutions in Rn,n=1,2,3. |
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| Keywords: | Existence-uniqueness Pattern theory Computational anatomy GRID model Macroscopic biological growth |
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