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Diffusive convective elliptic problem in variable exponent space and measure data

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  23 January 2025

Safimba Soma Open the ORCID record for Safimba Soma [Opens in a new window] ,
Ibrahime Konaté  and
Adama Kaboré
Safimba Soma*
Affiliation:
Laboratoire de Mathématiques et d’Informatique (LA.M.I), UFR, Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, 03 BP 7021 03 Ouagadougou, Burkina Faso
Ibrahime Konaté
Affiliation:
Laboratoire de Science et technologie (LaST), UFR, Sciences et Technologies, Université Thomas SANKARA, 12 BP 417 12 Ouagadougou, Burkina Faso e-mail: [email protected]
Adama Kaboré
Affiliation:
Laboratoire de Mathématiques et d’Informatique (LA.M.I), Institut des Sciences et de Technologie, Ecole Normale Superieure, 01 BP 1757 01 Ouagadougou, Burkina Faso e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

In this article, we study a class of convective diffusive elliptic problem with Dirichlet boundary condition and measure data in variable exponent spaces. We begin by introducing an approximate problem via a truncation approach and Yosida’s regularization. Then, we apply the technique of maximal monotone operators in Banach spaces to obtain a sequence of approximate solutions. Finally, we pass to the limit and prove that this sequence of solutions converges to at least one weak or entropy solution of the original problem. Furthermore, under some additional assumptions on the convective diffusive term, we prove the uniqueness of the entropy solution.

Keywords

Sobolev spacesvariable exponententropy solutionmaximal monotone graphRadon measure

MSC classification

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 24
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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