LEADER 04978nam 22006495 450 001 9910300145203321 005 20200706054504.0 010 $a3-319-05140-7 024 7 $a10.1007/978-3-319-05140-6 035 $a(CKB)2560000000149018 035 $a(EBL)1731643 035 $a(SSID)ssj0001204975 035 $a(PQKBManifestationID)11962954 035 $a(PQKBTitleCode)TC0001204975 035 $a(PQKBWorkID)11181050 035 $a(PQKB)10589610 035 $a(MiAaPQ)EBC1731643 035 $a(DE-He213)978-3-319-05140-6 035 $a(PPN)178321117 035 $a(EXLCZ)992560000000149018 100 $a20140419d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMethods of Small Parameter in Mathematical Biology /$fby Jacek Banasiak, Miros?aw Lachowicz 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (295 p.) 225 1 $aModeling and Simulation in Science, Engineering and Technology,$x2164-3679 300 $aDescription based upon print version of record. 311 $a3-319-05139-3 320 $aIncludes bibliographical references and index. 327 $a1 Small parameter methods ? basic ideas -- 2 Introduction to the Chapman?Enskog method ? linear models with migrations -- 3 Tikhonov?Vasilyeva theory -- 4 The Tikhonov theorem in some models of mathematical biosciences -- 5 Asymptotic expansion method in a singularly perturbed McKendrick problem -- 6 Diffusion limit of the telegraph equation -- 7 Kinetic model of alignment -- 8 From microscopic to macroscopic descriptions. - 9 Conclusion. 330 $aThis monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value.   The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques.   Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and  graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis. 410 0$aModeling and Simulation in Science, Engineering and Technology,$x2164-3679 606 $aDifferential equations 606 $aBiomathematics 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000 606 $aGenetics and Population Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/M31010 615 0$aDifferential equations. 615 0$aBiomathematics. 615 14$aOrdinary Differential Equations. 615 24$aMathematical and Computational Biology. 615 24$aGenetics and Population Dynamics. 676 $a515.35 700 $aBanasiak$b Jacek$4aut$4http://id.loc.gov/vocabulary/relators/aut$0314207 702 $aLachowicz$b Miros?aw$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300145203321 996 $aMethods of Small Parameter in Mathematical Biology$92512354 997 $aUNINA