Strong and variational formulations for evolutionary problem.

roblem

(Evolutionary
variational inequality problem) For a bounded set
with smooth boundary, time interval
and given functions
,
find a function
satisfying the
relationships
where the operation
is given by the definition (
Bilinear form B
2
) and the class of functions
is defined
by
We
introduce

Problem

(Strong formulation of
evolutionary problem) For a bounded set
with smooth boundary, time interval
and given functions
,
find a function
satisfying the
relationships
in
and
where the operator
is defined by the formula (
Operator L 2
).