LEADER 03808nam 22005895 450 001 9910299960603321 005 20220407192305.0 010 $a3-0348-0813-5 024 7 $a10.1007/978-3-0348-0813-2 035 $a(CKB)3710000000111983 035 $a(EBL)1730937 035 $a(OCoLC)883570895 035 $a(SSID)ssj0001242376 035 $a(PQKBManifestationID)11775485 035 $a(PQKBTitleCode)TC0001242376 035 $a(PQKBWorkID)11260675 035 $a(PQKB)11199011 035 $a(MiAaPQ)EBC1730937 035 $a(DE-He213)978-3-0348-0813-2 035 $a(PPN)178784508 035 $a(EXLCZ)993710000000111983 100 $a20140510d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic partial differential equations $evolume 2: reaction-diffusion equations /$fby Vitaly Volpert 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (796 p.) 225 1 $aMonographs in Mathematics,$x1017-0480 ;$v104 300 $aDescription based upon print version of record. 311 $a3-0348-0812-7 320 $aIncludes bibliographical references and indexes. 327 $aI. Introduction to the theory of reaction-diffusion equations -- Chapter 1. Reaction-diffusion processes, models and applications -- Chapter 2. Methods of analysis -- Chapter 3. Reaction-diffusion problems in bounded domains.- Chapter 4. Reaction-diffusion problems on the whole axis -- II. Reaction-diffusion waves in cylinders -- Chapter 5. Monotone systems -- Chapter 6. Reaction-diffusion problems with convection -- Chapter 7. Reaction-diffusion systems with different diffusion coefficients -- Chapter 8. Nonlinear boundary conditions -- Chapter 9. Nonlocal reaction-diffusion equations -- Chapter 10. Multi-scale models in biology -- Bibliographical comments -- Concluding remarks -- Acknowledgements -- References -- Index. 330 $aIf we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical analysis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered. 410 0$aMonographs in Mathematics,$x1017-0480 ;$v104 606 $aDifferential equations, Partial 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aDifferential equations, Partial. 615 14$aPartial Differential Equations. 676 $a515.353 676 $a515.3533 700 $aVolpert$b Vitaly$4aut$4http://id.loc.gov/vocabulary/relators/aut$060607 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299960603321 996 $aElliptic partial differential equations$9238560 997 $aUNINA