Abstract
In the space of functions with values in Hilbert space, we consider the Cauchy problem u′t + Au + B(u, u) = f(t), u(0) = 0, 0 ≤ t ≤ T. We construct examples of a self-adjoint operator A ≥ E and a bilinear transformation B satisfying the condition 〈B(u, v), v〉 = 0 such that the Cauchy problem is not strongly solvable.
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