LEADER 02801nam 2200577 450 001 9910480759303321 005 20180613001303.0 010 $a1-4704-0622-5 035 $a(CKB)3360000000465189 035 $a(EBL)3114126 035 $a(SSID)ssj0000889140 035 $a(PQKBManifestationID)11566330 035 $a(PQKBTitleCode)TC0000889140 035 $a(PQKBWorkID)10876184 035 $a(PQKB)10477043 035 $a(MiAaPQ)EBC3114126 035 $a(PPN)195418948 035 $a(EXLCZ)993360000000465189 100 $a20150417h20112011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aParabolic systems with polynomial growth and regularity /$fFrank Duzaar, Giuseppe Mingione, Klaus Steffen 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2011. 210 4$d©2011 215 $a1 online resource (118 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 214, Number 1005 300 $a"Volume 214, Number 1005 (first of 5 numbers )." 311 $a0-8218-4967-0 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Acknowledgments""; ""Introduction""; ""Chapter 1. Results""; ""1.1. Partial regularity""; ""1.2. Singular sets estimates""; ""1.3. Extended CalderA?³n-Zygmund theory""; ""1.4. Outline of the paper""; ""Chapter 2. Basic material, assumptions""; ""2.1. Notation, parabolic cylinders""; ""2.2. Basic assumptions, especially for partial regularity""; ""2.3. General technical results""; ""2.4. Compactness in parabolic spaces""; ""2.5. Function spaces, preliminaries""; ""2.6. Parabolic Hausdorff dimension""; ""Chapter 3. The A-caloric approximation lemma"" 327 $a""8.5. Proof of the a priori estimate""""8.6. Exit times""; ""8.7. Construction of comparison maps""; ""8.8. Estimates on cylinders""; ""8.9. Estimates for super-level sets""; ""8.10. Estimate 1.20 and proof of Theorem 1.6 concluded""; ""8.11. Proof of Theorem 1.5""; ""8.12. Proof of Theorems 1.7 and 1.9""; ""8.13. Interpolative nature of estimate 1.20""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 214, Number 1005. 606 $aDifferential equations, Parabolic 606 $aPolynomials 608 $aElectronic books. 615 0$aDifferential equations, Parabolic. 615 0$aPolynomials. 676 $a515.3534 700 $aDuzaar$b Frank$f1957-$0997178 702 $aMingione$b Giuseppe$f1972- 702 $aSteffen$b Klaus$f1945- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480759303321 996 $aParabolic systems with polynomial growth and regularity$92286799 997 $aUNINA LEADER 05265nam 2200673Ia 450 001 9910139959803321 005 20170809171555.0 010 $a1-282-37960-7 010 $a9786612379604 010 $a0-470-74998-9 010 $a0-470-74999-7 035 $a(CKB)1000000000822273 035 $a(EBL)470612 035 $a(OCoLC)535814139 035 $a(SSID)ssj0000343672 035 $a(PQKBManifestationID)11244859 035 $a(PQKBTitleCode)TC0000343672 035 $a(PQKBWorkID)10291606 035 $a(PQKB)11321069 035 $a(MiAaPQ)EBC470612 035 $a(PPN)139874658 035 $a(EXLCZ)991000000000822273 100 $a20090625d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aThermal convection$b[electronic resource] $epatterns, evolution, and stability (historical background and current status) /$fMarcello Lappa 210 $aHoboken, N.J. $cWiley$d2009 215 $a1 online resource (692 p.) 300 $aDescription based upon print version of record. 311 $a0-470-69994-9 320 $aIncludes bibliographical references and index. 327 $aThermal Convection; Contents; Preface; Acknowledgements; 1 Equations, General Concepts and Methods of Analysis; 1.1 Pattern Formation and Nonlinear Dynamics; 1.1.1 Some Fundamental Concepts: Pattern, Interrelation and Scale; 1.1.2 PDEs, Symmetry and Nonequilibrium Phenomena; 1.2 The Navier-Stokes Equations; 1.2.1 A Satisfying Microscopic Derivation of the Balance Equations; 1.2.2 A Statistical Mechanical Theory of Transport Processes; 1.2.3 The Continuity Equation; 1.2.4 The Momentum Equation; 1.2.5 The Total Energy Equation; 1.2.6 The Budget of Internal Energy; 1.2.7 Newtonian Fluids 327 $a1.2.8 Some Considerations About the Dynamics of Vorticity1.2.9 Incompressible Formulation of the Balance Equations; 1.2.10 Nondimensional Form of the Equations for Thermal Problems; 1.3 Energy Equality and Dissipative Structures; 1.4 Flow Stability, Bifurcations and Transition to Chaos; 1.5 Linear Stability Analysis: Principles and Methods; 1.5.1 Conditional Stability and Infinitesimal Disturbances; 1.5.2 The Exponential Matrix and the Eigenvalue Problem; 1.5.3 Linearization of the Navier-Stokes Equations 327 $a1.5.4 A Simple Example: The Stability of a Parallel Flow with an Inflectional Velocity Profile1.5.5 Weaknesses and Limits of the Linear Stability Approach; 1.6 Energy Stability Theory; 1.6.1 A Global Budget for the Generalized Disturbance Energy; 1.6.2 The Extremum Problem; 1.7 Numerical Integration of the Navier-Stokes Equations; 1.7.1 Vorticity Methods; 1.7.2 Primitive Variables Methods; 1.8 Some Universal Properties of Chaotic States; 1.8.1 Feigenbaum, Ruelle-Takens and Manneville-Pomeau Scenarios; 1.8.2 Phase Trajectories, Attractors and Strange Attractors 327 $a1.8.3 The Lorenz Model and the Butterfly Effect1.8.4 A Possible Quantification of SIC: The Lyapunov Spectrum; 1.8.5 The Mandelbrot Set: The Ubiquitous Connection Between Chaos and Fractals; 1.9 The Maxwell Equations; 2 Classical Models, Characteristic Numbers and Scaling Arguments; 2.1 Buoyancy Convection and the Boussinesq Model; 2.2 Convection in Space; 2.2.1 A Definition of Microgravity; 2.2.2 Experiments in Space; 2.2.3 Surface Tension-driven Flows; 2.2.4 Acceleration Disturbances on Orbiting Platforms and Vibrational Flows; 2.3 Marangoni Flow 327 $a2.3.1 The Genesis and Relevant Nondimensional Numbers2.3.2 Microzone Facilities and Microscale Experimentation; 2.3.3 A Paradigm Model: The Liquid Bridge; 2.4 Exact Solutions of the Navier-Stokes Equations for Thermal Problems; 2.4.1 Thermogravitational Convection: The Hadley Flow; 2.4.2 Marangoni Flow; 2.4.3 Hybrid States; 2.4.4 General Properties; 2.4.5 The Infinitely Long Liquid Bridge; 2.4.6 Inclined Systems; 2.5 Conductive, Transition and Boundary-layer Regimes; 3 Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology 327 $a3.1 Technological Processes: Small-scale Laboratory and Industrial Setups 330 $aThermal Convection - Patterns, Stages of Evolution and Stability Behavior provides the reader with an ensemble picture of the subject, illustrating the state-of-the-art and providing the researchers from universities and industry with a basis on which they are able to estimate the possible impact of a variety of parameters. Unlike earlier books on the subject, the heavy mathematical background underlying and governing the behaviors illustrated in the text are kept to a minimum. The text clarifies some still unresolved controversies pertaining to the physical nature of the dominatin 606 $aThermal conductivity 606 $aDensity currents 606 $aViscous flow 606 $aFluid dynamics 615 0$aThermal conductivity. 615 0$aDensity currents. 615 0$aViscous flow. 615 0$aFluid dynamics. 676 $a541.36 676 $a620.11296 700 $aLappa$b Marcello$0964709 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139959803321 996 $aThermal convection$92288639 997 $aUNINA