Well-posedness and asymptotic behaviour of a non-dissipative beam equation with a quotient space method

A beam equation model is studied, for which no suitable dissipative norm can be associated but only a semi-norm, vanishing on some subspace. Considering a quotient by that subspace creates dissipativity which guarantees well posedness of this problem. Asymptotic behaviour is also obtained by using the quotient. The linear problem, involving high-order multiplier is studied and then the non-linear problem, thanks to the artificial problem method. Copyright