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03-Doctorat

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Browsing 03-Doctorat by Author "Abbad, Abir"

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    Dynamics of a Turing -type reaction - diffusion model
    (2021) Abbad, Abir
    The aimofthisthesisistostudythedynamicsofaTuring-typereaction-di usion model,i.e.studyareaction-di usionmodelthatexhibitsTuringproperties,whereas the reaction-di usionde nesthemechanisminwhichseveralinteractingchemicalsor agentsreacttogetherwhiledi usingorspreadingacrossaliquidorgaseousmedium simultaneously,usually,theseprocessesarestudiedfortheirabilitytoproducenontrivial patterns thatevolveovertime.Suchpatternsaredrivenbydi usion,alsoreferredtoas TuringstructuresorTuringpatterns.TheTuringpatternsaremeasuredinthepresenceof di usion, butarenotpresentintheabsenceofdi usion,thismechanismecalled"di usion- driveninstability"or"Turinginstability".Inthiswork,thestudywasrelated"thewell- knownDegn-Harrisonreactiondi usionmodelanditsgeneralization".Ourthechniqueto provetheasymptoticstabilityofthesteadystatesolutionisbasedontheeigen-analysis, the Poincar e{BendixsontheoremandthedirectLyapunovmethod.