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《Traveling Wave Solutions for Bistable Differential-Difference Equations with Periodic Diffusion》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、SIAMJ.APPL.MATH.c2001SocietyforIndustrialandAppliedMathematicsVol.61,No.5,pp.1648–1679TRAVELINGWAVESOLUTIONSFORBISTABLEDIFFERENTIAL-DIFFERENCEEQUATIONSWITHPERIODICDIFFUSION?CHRISTOPHERE.ELMER?ANDERIKS.VANVLECK?Abstract.Weconsidertravelingwavesolutionstospatiallydiscretereaction-di?usio
2、nequationswithnonlocalvariabledi?usionandbistablenonlinearities.To?ndthetravelingwavesolutionsweintroduceanansatzinwhichthewavespeeddependsontheunderlyinglatticeaswellasontime.Forthecaseofspatiallyperiodicdi?usionweobtainanalyticsolutionsforthetravelingwaveproblemusingapiecewiselinearno
3、nlinearity.Theformulaforthewaveformsisimplicitlyde?nedinthegeneralperiodiccaseandweprovideanexplicitformulaforthecaseofperiodtwodi?usion.Wepresentnumericalstudiesfortimet=0?xedandforthetimeevolutionofthetravelingwaves.Whent=0westudythecasesofhomogeneous,periodtwo,andperiodfourdi?usionco
4、e?cientsusingacubicnonlinearity,anduncover,numerically,aperioddoublingbifurcationinthewavespeedversusdetuningparameterrelation.Forthetimeevolutioncasewealsodiscoveradetuningparameterdependentbifurcationinobservedphenomena,whichisaproductofboththenonlocaldi?usionoperatorandthespinodale?e
5、ctsofthenonlinearity.Keywords.travelingwaves,propogationfailure,bistableequation,periodicdi?usionAMSsubjectclassi?cations.35K57,74N99PII.S00361399993571131.Introduction.Problemsthataremodeledbynonlinearspatiallydiscretedif-fusionequationsoccurinmanyareasofscience.Inthematerialssciencese
6、xamplesincludecrystalgrowth,interfacemotionincrystallinematerials,spinodaldecompo-sition,andgrainboundarymovementinthin?lms.Spatiallydiscretedi?usionop-eratorsallowthematerialbeingmodeledtobedescribedintermsofitsunderlyingcrystallinelattice.Phenomenasuchascrystallographicpinningandlatti
7、ceanisotropy,phenomenathatareoftenaddedtospatiallycontinuousmodelsinan“adhoc”man-ner,occurnaturallyinspatiallydiscretematerialsmodels.Inbiology,examplesofapplicationsofspatiallydiscretemodelsincludethebidomainmodelforcardiactissue(de?brillation),tissue?ltration,gasexchangeinlun
