Integral state-constrained optimal control problems for some quasilinear parabolic equations

The state-constrained optimal control problems of systems governed by some quasilinear parabolic equations in divergence form are studied. A hypotheses is established in terms of polynomial growth conditions on the functions involved. The results are easier to apply and it avoids the possibility of finding hidden difficulties in terms of abstract assumptions. Moreover, it provides concrete examples within the framework and out of the scope of previous known works.