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Zbl 0737.35135
Byszewski, Ludwik
Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functionals.
(English)
[J] J. Math. Anal. Appl. 156, No.2, 457-470 (1991). ISSN 0022-247X

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 $$u\sp i\sb t(x,t)\le f\sp i(x,t,u(x,t), u\sp i\sb x(x,t), u\sp i\sb{xx}(x,t);[u])\hbox { for a.e. } (x,t)$$ $i=1,\ldots,m$; $u=(u\sp 1,\ldots,u\sp m)$, with some additional nonlocal assumptions is discussed. Here $f\sp i(\cdots;[u])$ are functionals with respect to $u$.
[U.Raitums (Riga)]
MSC 2000:
*35R10 Difference-partial differential equations
35B50 Maximum principles (PDE)

Keywords: maximum principle; nonlocal parabolic inequalities

Cited in: Zbl 0774.35038

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