for Discontinuously Coupled
Systems of Evolution Variational Inequalities and Application
By: Siegfried Carl, Seppo Heikkila, and Joseph W. Jerome
We consider initial-boundary value problems for
weakly coupled systems of parabolic equations
under coupled nonlinear flux boundary condition.
Both coupling vector fields f,g
are assumed to be either of competitive or cooperative type,
but may otherwise be discontinuous with respect to all their arguments.
The main goal is to provide conditions for the vector fields f
and g that allow
the identification of regions of existence of solutions
(so called trapping regions). To this end the problem is
transformed to a discontinuously coupled system of evolution variational
a generalized outward pointing vector field on the boundary
of a rectangle of the dependent variable space, the system
of evolution variational inequalities is solved via a fixed
point problem for some increasing
operator in an appropriate ordered Banach space.
The main tools used in the proof are evolution variational
inequalities, comparison techniques, and fixed point results
in ordered Banach spaces.
This paper has appeared: J. Math. Anal. Appl. 282 (2003), 421--435, and
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