Blowup solutions for a reaction–diffusion system with exponential nonlinearities

Tej-eddine Ghoul, Van Tien Nguyen, Hatem Zaag

    Research output: Contribution to journalArticle

    Abstract

    We consider the following parabolic system whose nonlinearity has no gradient structure: {∂tu=Δu+epv,∂tv=μΔv+equ,u(⋅,0)=u0,v(⋅,0)=v0,p,q,μ>0, in the whole space RN. We show the existence of a stable blowup solution and obtain a complete description of its singularity formation. The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. In particular, our analysis uses neither the maximum principle nor the classical methods based on energy-type estimates which are not supported in this system. The stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem.

    Original languageEnglish (US)
    Pages (from-to)7523-7579
    Number of pages57
    JournalJournal of Differential Equations
    Volume264
    Issue number12
    DOIs
    StatePublished - Jun 15 2018

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    Maximum principle
    Blow-up Solution
    Reaction-diffusion System
    Nonlinearity
    Index Theory
    Parabolic Systems
    Maximum Principle
    Blow-up
    Singularity
    Gradient
    Energy
    Estimate
    Interpretation

    Keywords

    • Blowup profile
    • Blowup solution
    • Semilinear parabolic system
    • Stability

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Blowup solutions for a reaction–diffusion system with exponential nonlinearities. / Ghoul, Tej-eddine; Nguyen, Van Tien; Zaag, Hatem.

    In: Journal of Differential Equations, Vol. 264, No. 12, 15.06.2018, p. 7523-7579.

    Research output: Contribution to journalArticle

    Ghoul, Tej-eddine ; Nguyen, Van Tien ; Zaag, Hatem. / Blowup solutions for a reaction–diffusion system with exponential nonlinearities. In: Journal of Differential Equations. 2018 ; Vol. 264, No. 12. pp. 7523-7579.
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