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In this work, we are concerned with a class of elliptic problems with both absorption terms and critical growth in the gradient. We suppose that the data belong to Lm() with m > n/2 and we prove the existence of bounded weak solutions via L1-estimates. A priori estimates and Stampacchia's L1-regularity are our main ingredient. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study a non-local initial boundary-value problem arising in Ohmic heating. By using a dynamical systems approach, some existence and uniqueness results are proved and the existence of a compact attractor is shown. [ABSTRACT FROM AUTHOR]