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Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functionals. (English) Zbl 0737.35135

The paper looks for a new object for which an analogue of the maximum principle for solutions of parabolic equations is valid. The case of noncylindrical domains and nonlocal parabolic inequalities of the type

u t i (x,t)f i (x,t,u(x,t),u x i (x,t),u xx i (x,t);[u])fora.e.(x,t)

i=1,...,m; u=(u 1 ,...,u m ), with some additional nonlocal assumptions is discussed. Here f i (;[u]) are functionals with respect to u.

Reviewer: U.Raitums (Riga)

MSC:
35R10Partial functional-differential equations
35B50Maximum principles (PDE)