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Existence Result for Triangular Reaction—Diffusion Systems with L1 Data and Critical Growth with Respect to the Gradient

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Abstract

In this paper we prove the existence of weak solutions for m × m reaction-diffusion systems for which two main properties hold: the positivity of the solutions and the triangular structure. Moreover, the nonlinear terms have critical growth with respect to the gradient.

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Authors and Affiliations

  1. Laboratory LAMAI, Faculty of Science and Technology of Marrakech, B.P. 549, Av. Abdelkarim Elkhattabi, 40000, Marrakech, Morroco

    Nour Eddine Alaa

  2. Department of Mathematics, The University Ferhat Abbas, Ain Arnet Street, Setif, 19000, Algeria

    Mosbahi Salim

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  1. Nour Eddine Alaa
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  2. Mosbahi Salim
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Correspondence to Nour Eddine Alaa.

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Alaa, N.E., Salim, M. Existence Result for Triangular Reaction—Diffusion Systems with L1 Data and Critical Growth with Respect to the Gradient. Mediterr. J. Math. 10, 255–275 (2013). https://doi.org/10.1007/s00009-012-0238-9

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  • DOI: https://doi.org/10.1007/s00009-012-0238-9

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