Parabolic equations in Musielak - Orlicz spaces with discontinuous in time N-function

摘要: Abstract We consider a parabolic PDE with Dirichlet boundary condition and monotone operator A non-standard growth controlled by an N-function depending on time spatial variable. do not assume continuity in for the N-function. Using additional regularization effect coming from equation, we establish existence of weak solutions particular case isotropic N-function, also prove their uniqueness. This general result applies to equations studied literature like p ( t , x ) -Laplacian double-phase problems.