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Abstract
Consider the evolution equation
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
where K(u) is a positive continuously differentiable function defined on (0,(INFIN)). The operator K is shown to be closed and dissipative on the domain
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
almost everwhere, for some function g(epsilon)L('1)(R('1)) with (INT)g = 0}. Also, the following is shown:
R((lamda)I-K) (R-HOOK) D(K).
The theorem of Crandall and Liggett on the generation of nonlinear semi-groups given a semi-group solution, u, to (E). This semi-group solution is also a weak solution to (E). Some properties of D(K) are exhibited. Under more conditions on K and D(K) the u is a classical solution. u is shown to be the transition probability density of a special type of Markov processe with "non-constant transition mechanisms."
