We treat the existence of a weak solution for the equation when in the following background:-We assume the existence of the Gelfand triple V c H c V * V, being a real, separable Hilbert space, V* its dual and H , a real Hilbert space identified with its dual.-U ( t ) is a strongly continuous semigroup of operators, on both H and v*.-A is an operator mapping V into V* -B is a linear (not necessarily continuous) operator from H to H.
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