LEADER 03888nam 22005055 450 001 9910300100103321 005 20200705125921.0 010 $a3-030-01506-8 024 7 $a10.1007/978-3-030-01506-0 035 $a(CKB)4100000007159054 035 $a(MiAaPQ)EBC5603005 035 $a(DE-He213)978-3-030-01506-0 035 $a(PPN)232471282 035 $a(EXLCZ)994100000007159054 100 $a20181121d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTheory and Applications of Abstract Semilinear Cauchy Problems /$fby Pierre Magal, Shigui Ruan 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (558 pages) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v201 311 $a3-030-01505-X 320 $aIncludes bibliographical references and index. 327 $aChapter 1- Introduction -- Chapter 2- Semigroups and Hille-Yosida Theorem -- Chapter 3- Integrated Semigroups and Cauchy Problems with Non-dense Domain -- Chapter 4- Spectral Theory for Linear Operators -- Chapter 5- Semilinear Cauchy Problems with Non-dense Domain -- Chapter 6- Center Manifolds, Hopf Bifurcation and Normal Forms -- Chapter 7- Functional Differential Equations -- Chapter 8- Age-structured Models -- Chapter 9- Parabolic Equations -- References -- Index. 330 $aSeveral types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v201 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 14$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 676 $a515.353 700 $aMagal$b Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767931 702 $aRuan$b Shigui$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300100103321 996 $aTheory and Applications of Abstract Semilinear Cauchy Problems$92065743 997 $aUNINA