LEADER 03673nam 2200601 a 450 001 9910816632303321 005 20230721024359.0 010 $a1-282-75835-7 010 $a9786612758355 010 $a981-4277-70-3 035 $a(CKB)2490000000001651 035 $a(DLC)2010485269 035 $a(StDuBDS)AH24686379 035 $a(SSID)ssj0000424205 035 $a(PQKBManifestationID)12209721 035 $a(PQKBTitleCode)TC0000424205 035 $a(PQKBWorkID)10470207 035 $a(PQKB)10032567 035 $a(MiAaPQ)EBC1681229 035 $a(WSP)00000570 035 $a(Au-PeEL)EBL1681229 035 $a(CaPaEBR)ebr10422166 035 $a(CaONFJC)MIL275835 035 $a(OCoLC)729020139 035 $a(EXLCZ)992490000000001651 100 $a20100924d2009 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear systems of partial differential equations$b[electronic resource] $eapplications to life and physical sciences /$fAnthony W. Leung 210 $aHackensack, N.J. $cWorld Scientific$dc2009 215 $a1 online resource (xii, 532 p. ) $cill 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-4277-69-X 320 $aIncludes bibliographical references and index. 327 $aPositive solutions for systems of two equations -- Positive solutions for large systems of equations -- Optimal control for nonlinear systems of partial differential equations -- Persistence, upper and lower estimates, blowup, cross-diffusion and degeneracy -- Traveling waves, systems of waves, invariant manifolds, fluids and plasma -- Appendices. 330 $aThe book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W2ptheory. Introductory explanations are included in the appendices for non-expert readers. The first chapter covers a wide range of steady-state and stability results involving prey-predator, competing and cooperating species under strong or weak interactions. Many diagrams are included to easily understand the description of the range of parameters for coexistence. The book provides a comprehensive presentation of topics developed by numerous researchers. Large complex systems are introduced for modern research in ecology, medicine and engineering. Chapter 3 combines the theories of earlier chapters with the optimal control of systems involving resource management and fission reactors. This is the first book to present such topics at research level. Chapter 4 considers persistence, cross-diffusion, and boundary induced blow-up, etc. The book also covers traveling or systems of waves, coupled Navier-Stokes and Maxwell systems, and fluid equations of plasma display. These should be of interest to life and physical scientists. 606 $aDifferential equations, Partial 606 $aDifferential equations, Nonlinear 615 0$aDifferential equations, Partial. 615 0$aDifferential equations, Nonlinear. 676 $a515.35 686 $aSK 540$2rvk 700 $aLeung$b Anthony W.$f1946-$042495 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816632303321 996 $aNonlinear systems of partial differential equations$9230658 997 $aUNINA