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

Abstrakt

We consider a parabolic PDE with Dirichlet boundary condition and monotone operator A with non -standard growth controlled by an N-function depending on time and spatial variable. We do not assume continuity in time for the N-function.

Using an additional regularization effect coming from the equation, we establish the existence of weak solutions and in the particular case of isotropic N-function, we also prove their uniqueness. This general result applies to equations studied in the literature like p(t, x)-Laplacian and double-phase problems.

Klíčová slova

• Parabolic equation
• Non-standard growth
• Discontinuous N-function
• Existence
• Uniqueness