简介：Inthispaper,adifferenceschemewithnonuniformmeshesisestablishedfortheinitial-boundaryproblemofthenonlinearparabolicsystem.Itisprovedthatthedifferenceschemeissecondorderconvergentinspacestepandtimestep.

简介：Thispaperstudiesthenonlinearvariationalinequalitywithintegro-differentialtermarisingfromvaluationofAmericanstyledoublebarrieroption.First,theauthorsusethepenaltymethodtotransformthevariationalinequalityintoanonlinearparabolicinitialboundaryproblem(i.e.,penaltyproblem).Second,theexistenceanduniquenessofsolutiontothepenaltyproblemareprovedbyusingtheScheaferfixedpointtheory.Third,theauthorsprovetheexistenceofvariationalinequality'solutionbyshowingthefactthatthepenalizedPDEconvergestothevariationalinequality.Theuniquenessofsolutiontothevariationalinequalityisalsoprovedbycontradiction.

简介：Theproblemofconstructingamodelreferenceadaptivecontrollawforanuncertain1-dimensionalparabolicsystemisconsideredinthisarticle.Thecontrollerdesignedhereinvolvesonlytheplantstatebutnoitsderivatives.Aprioriboundsontheplant'suncertainparametersareusedtoproposeswitchinglawswhichserveasanadaptivemechanism.Theexponentialdecaytozeroofthestateerrorwithanyprescribedrateisguaranteedbychoosingacontrollerparametercorrespondingly.Numericalstudiesarealsopresentedtoillustratetheapplicabilityofthecontrollaw.