We study a class of second-order nonlocal degenerate semilinear reaction-diffusion equations with general nonlinear diffusion term. Under a set of conditions on the general nonlinear diffusivity and nonlinear nonlocal source term, we prove global existence and uniqueness results in a subset of a Sobolev space. Furthermore, we prove nonexistence of smooth solution or blow-up of solution under some other set of conditions. Lastly, we give illustrative examples for which our results apply. 2000

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... hematics Subject Classification. 35K05, 35K10, 35K20, 35K58, 35K65. Key words and phrases. Initial boundary value problems; Galerkin approximations; energy estimates; Banach fixed point theorem; existence and uniqueness of weak solutions.