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10
Preface
distancedeterminationoforientationanddimensionsofplanecracks,
boundedbyaclosedsmoothcontour,aregiven.
InChapter4theinversescatteringproblemsforathin-walledtun-
nelplaneinclusionsofasmallandlargerigidityarestudied.Modelsof
interactionofathin-walledinclusionwithamatrixaredescribedand
thecorrespondingintegro-differentialequationsofthedirectscattering
problemsareconstructed.Theseresultsareusedfurtherforsolvingof
theinverseproblems.Asolutionoftheproblemofdistancedetermina-
tionofdimensionsofathin-walledabsolutelyrigidstripinclusions,and
alsoformulaeforintensitystressescoefficientsinashort-wavedomain
aredescribed.Theinverseproblemofscatteringbyaplanethin-walled
inclusionofalargerigidityisconsidered,wherephysical-mechanicalpa-
rametersoftheinclusionanditsdimensionsareunknown.Fordetermi-
nationofthelatter,anelasticwavenon-specularreflectioneffectisused,
thathasbeentheoreticallygroundedforthesituationbeingconsidered,
probably,forthefirsttime.Aproblemofdistancedeterminationofthe
dimensionsandthematerialparametersofathin-walledstripinclusions
ofalowrigidityissolved,andhigh-frequencyasymptoticsofeffective
characteristicsofstressesneartipsofinhomogeneitiesareconsidered.
Chapter5concernsanalysisofthedistancedeterminationofthege-
ometricalparametersofvolumetricclosedscatterers.Usingtheitera-
tiveregularizationonthebasisoftheNewton-Kantorovichmethod,an
effectivenumerical-analyticalmethodoftheformreconstructionfora
volumetricbodyisconstructed.
InChapter6,usingalong-andshort-waveasymptoticsofasolution
ofcorrespondingdirectscatteringproblems,thescalarinverseproblems
areconsidered.Differentapproximationmethodsofsolvingoftheinverse
problemsgiveninthischapterareillustratedbythenumericalexamples.
Thebookpresentsclearandelegantmethodsandisaimedatgrad-
uate,postgraduatestudentsoftheinformationtechnologyfacultiesand
researchersindomainofmathematical-numericalmodelling.
Lodz,2013V.F.Emets,J.Rogowski
