Browsing by Author "Alves, Claudianor O."

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    Existence and uniqueness of solution for some time fractional parabolic equations involving the 1-Laplace operator
    (Springer, 2023) Alves, Claudianor O.; Boudjeriou, Tahir
    This paper is devoted to study the time fractional parabolic 1-Laplacian type. Firstly, by using the parabolic regularization technique and approximating the parabolic 1-Laplacian problem by a class of parabolic equations of p-Laplacian type with p> 1 , we establish the existence of global weak radial solutions to the considered problem for a wide class of nonlinearities. Secondly, we discuss the extinction property of solutions to the time fractional total variation flow (FTVF) with different boundary conditions (Dirichlet and Neumann conditions). We conclude this paper by providing an example of explicit solution to the (FTVF)
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    Existence of solution and qualitative behavior for a class of heat equations
    (Elsevier, 2024) Alves, Claudianor O.; Boudjeriou, Tahir; Prado, Humberto
    The objective of this paper is to investigate the existence of solutions and their qualitative behavior for a given class of nonlinear evolutionary equations. We demonstrate that the pseudo-differential operator Δexp⁡(−cΔ) acts as the infinitesimal generator of the solution operator. Here, Δ denotes the Euclidean Laplace operator, and c is a positive constant. We establish the appropriate domain for the operator Δexp⁡(−cΔ) and prove that it generates a C0 semigroup on L2(RN). Additionally, we introduce a scale of spaces wherein smooth solutions exist, and these spaces are continuously embedded into the Sobolev class. Finally, we investigate the nonlinear evolution problem for a broad class of nonlinearities.
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    Existence of solution for a class of heat equation involving the 1-Laplacian operator
    (Elsevier, 2022) Alves, Claudianor O.; Boudjeriou, Tahir
    This paper concerns the existence of global solutions for the following class of heat equations involving the 1-Laplacian operator for the Dirichlet problem {ut−Δ1u=f(u)inΩ×(0,+∞),u=0in∂Ω×(0,+∞),u(x,0)=u0(x)inΩ, where Ω⊂RN is a smooth bounded domain, N≥1, f:R→R is a continuous function satisfying some technical conditions and [Formula presented] denotes the 1-Laplacian operator. The existence of global solutions is done by using an approximation technique that consists in working with a class of p-Laplacian problems associated with (P) and then taking the limit when p→1+ to get our results
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    Global existence for parabolic p-Laplace equations with supercritical growth in whole RN
    (Elsevier, 2024) Alves, Claudianor O.; Boudjeriou, Tahir
    The focus of this paper is to investigate the global existence and uniqueness of weak solutions for a class of parabolic p-Laplacian equations whose nonlinearity has a supercritical growth.