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with the function ψ satisfying some conditions and the problem is supplemented with boundary conditions of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for f ∈ L(D) there exists a unique solution u such that u, ∂tu, ∂ xu ∈ L (D) , j = 1, 2. The proof is based on the domain decomposition method. This work complements the results obtained in [10].

Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains