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In this paper, we study existence, uniqueness and stability questions for the nonlinear parabolic equation: ∂u/∂t - Δpu + α(u) = f in ]0, T[xΩ, with Neumann-type boundary conditions and initial data in L¹. Our approach is based essentially on the time discretization technique by Euler forward scheme. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in [L∞(Ω)]² and ... [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in [L∞(Ω)]² and... [ABSTRACT FROM AUTHOR]

We study the doubly nonlinear parabolic equation ∂β(u)/∂t - Δpu + f(x, t, u) = 0 in Ω x R+, with Dirichlet boundary conditions and initial data. We investigate a time-discretization of the continuous problem by the Euler forward scheme. In addition to proving existence, uniqueness and stability questions, we study the long time behavior of the solution to the discrete problem. We prove the existence of a global attractor, and obtain its regularity under additional conditions. [ABSTRACT FROM AUTHOR]