Energy methods for free boundary problems: applications to nonlinear PDEs and fluid mechanics
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2002
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
48 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 329 S. |
| ISBN: | 0817641238 3764341238 |
Internformat
MARC
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| 245 | 1 | 0 | |a Energy methods for free boundary problems |b applications to nonlinear PDEs and fluid mechanics |c S. N. Antontsev ; J. I. Diaz ; S. Shmarev |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2002 | |
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Datensatz im Suchindex
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| adam_text | S.N. ANTONTSEV J.I. DIAZ S. SHMAREV ENERGY METHODS FOR FREE BOUNDARY
PROBLEMS APPLICATIONS TO NONLINEAR PDES AND FLUID MECHANICS BIRKHAUSER
BOSTON * BASEL * BERLIN CONTENTS PREFACE IX 1 LOCALIZED SOLUTIONS OF
NONLINEAR STATIONARY PROBLEMS 1 1 INTRODUCTION 1 1.1 A HEURISTIC
EXPLANATION OF THE METHOD .,_ 2 1.2 A FEW EXAMPLES OF LOCALIZED
SOLUTIONS 8 2 SECOND-ORDER ELLIPTIC EQUATIONS 10 2.1 GENERAL LOCAL
THEOREMS: THE DIFFUSION/ABSORPTION BALANCE . 10 2.2 COMPLETION OF THE
PROOF OF THEOREM 2.1 * * * * 18 3 THE WEIGHTED DIFFUSION/ABSORPTION
BALANCE 25 3.1 GLOBAL APPLICATIONS: LOCALIZED SOLUTIONS OF THE
ASSOCIATED BOUNDARY-VALUE PROBLEMS: THE CYLINDER DOMAINS 28 4
ANISOTROPIC EQUATIONS: DIFFUSION/ABSORPTION BALANCE 39 4.1 LOCALIZATION
VIA DIFFUSION/ABSORPTION BALANCE 39 4.2 ONE-DIRECTIONAL PHENOMENA 43 5
SYSTEMS OF SECOND-ORDER ELLIPTIC EQUATIONS 46 6 HIGHER-ORDER ELLIPTIC
EQUATIONS 52 6.1 PLANE ENERGY SETS 54 6.2 RADIAL ENERGY SETS 63 7
BIBLIOGRAPHICAL NOTES AND OPEN PROBLEMS 65 2 STABILIZATION IN A FINITE
TIME TO A STATIONARY STATE 69 1 INTRODUCTION 69 1.1 ILLUSTRATIVE
EXAMPLES 71 VI CONTENTS 2 SECOND-ORDER PARABOLIC EQUATIONS 78 2.1
EQUATIONS IN BOUNDED DOMAINS 78 2.2 THE ENERGY RELATION 80 2.3 FINITE
TIME EXTINCTION 82 3 THE WEIGHTED DIFFUSION-ABSORPTION BALANCE 91 4 THE
CAUCHY PROBLEM 94 5 EQUATIONS WITH NONPOWER AND ISOTROPIC NONLINEARITIES
97 5.1 ISOTROPIC NONLINEAR TERMS 97 5.2 LOGARITHMIC NONLINEARITY 98 5.3
EQUATIONS WITH ANISOTROPIC NONLINEARITY 99 5.4 EQUATIONS THAT DEGENERATE
IN A SEPARATE DIRECTION 103 6 SYSTEMS OF EQUATIONS OF COMBINED TYPE 104
7 HIGHER-ORDER PARABOLIC EQUATIONS AND OTHER APPLICATIONS 108 7.1
HIGHER-ORDER PARABOLIC EQUATIONS 108 7.2 NONLOCAL OPERATORS 110 7.3
EQUATIONS WITH SINGULAR SUPERABSORPTION TERMS ILL 7.4 FINITE TIME
STABILIZATION TO A NONZERO STATE ILL 8 BIBLIOGRAPHICAL NOTES AND OPEN
PROBLEMS 114 3 SPACE AND TIME LOCALIZATION IN NONLINEAR EVOLUTION
PROBLEMS 119 1 INTRODUCTION 119 1.1 DEFINITIONS 119 1.2 EXAMPLES 122 1.3
SCHEME OF THE METHOD 124 1.3.1 FINITE SPEED OF PROPAGATION OF
DISTURBANCES . . . 126 1.3.2 THE WAITING TIME EFFECT 129 2 GENERAL
SECOND-ORDER EQUATIONS 130 2.1 FINITE SPEED OF PROPAGATION 130 2.2
STABLE LOCALIZATION 142 3 THE WAITING TIME PROPERTY 146 4 SHRINKING OF
SUPPORTS AND FORMATION OF A DEAD CORE 150 4.1 THE ENERGY RELATION:
INTEGRATION-BY-PARTS FORMULA 153 4.2 DIFFERENTIAL INEQUALITIES 154 4.3
ANALYSIS OF THE DIFFERENTIAL INEQUALITIES 161 4.4 ESTIMATES ON THE TOTAL
ENERGY . 162 4.5 THE ONE-DIRECTIONAL PHENOMENA: LOCALIZATION VIA
DIFFUSION- CONVECTION BALANCE 165 5 EQUATIONS WITH NONHOMOGENEOUS
ABSORPTION TERMS 171 6 EQUATIONS WITH ANISOTROPIC NONLINEARITIES 175 7
SYSTEMS OF PARABOLIC EQUATIONS 179 8 HIGHER-ORDER PARABOLIC EQUATIONS
180 8.1 LOCALIZATION IN SPACE 181 8.2 DECAY RATES AS T * OO AND
EXTINCTION IN FINITE TIME .... 188 9 BIBLIOGRAPHICAL NOTES 189 CONTENTS
VII APPLICATIONS TO PROBLEMS IN FLUID MECHANICS 193 1 INTRODUCTION 193 2
THE BALANCE LAWS OF FLUID MECHANICS 194 3 STATIONARY PROBLEMS OF GAS
DYNAMICS WITH FREE BOUNDARIES . . . . 198 3.1 GOVERNING EQUATIONS 198
3.2 HOMOGENEOUS BOUNDARY CONDITIONS: AXIS-SYMMETRIC FLOWS 202 3.3
NONHOMOGENEOUS BOUNDARY CONDITIONS: PLANE CASE . . . . 207 4 TWO-PHASE
FILTRATION OF IMMISCIBLE INCOMPRESSIBLE FLUIDS . . . . 209 4.1
MATHEMATICAL MODEL 209 4.2 STABILIZATION TO A CONSTANT PROFILE IN A
FINITE TIME 213 4.3 FINITE SPEED OF PROPAGATION AND THE WAITING TIME
EFFECT . . 216 5 FLOWS OF GAS WITH DENSITY-DEPENDENT VISCOSITY 219 5.1
MAIN EQUATIONS 219 5.2 FINITE SPEED OF PROPAGATION AND THE WAITING TIME
EFFECT . . 222 6 VISCOUS-ELASTIC MEDIA 224 6.1 NONLINEAR ONE-DIMENSIONAL
VISCOUS-ELASTICITY EQUATION . .224 6.2 FINITE SPEED OF PROPAGATION AND
THE WAITING TIME EFFECT . . 225 7 FLOWS OF NONHOMOGENEOUS NON-NEWTONIAN
FLUID 227 7.1 GOVERNING EQUATIONS 227 7.2 PSEUDOPLASTIC FLUIDS:
LOCALIZATION IN TIME 229 7.3 PSEUDOPLASTIC FLUID WITH VANISHING OR
UNBOUNDED DENSITY . 233 7.3.1 FORMULATION OF THE PROBLEM 233 7.3.2
ESTIMATES FOR THE ENERGY FUNCTION 234 7.3.3 LOCALIZATION IN A FINITE
TIME 235 7.4 FLOWS WITH NONLINEAR SOURCES 238 7.5 SPACE LOCALIZATION IN
DILATANT FLUIDS . 239 7.6 A FLOW OF AN IDEAL NON-NEWTONIAN FLUID IN A
PIPE 240 8 BOUNDARY LAYERS IN DILATANT FLUID 242 9 BOUSSINESQ SYSTEM
INVOLVING NONLINEAR THERMAL DIFFUSION . . . . 245 9.1 THE MODEL 245 9.2
SPATIAL LOCALIZATION 247 9.3 PROOFS OF THEOREMS 9.1 AND 9.2 248 9.4 TIME
LOCALIZATION 254 10 SIMULTANEOUS MOTION IN THE SURFACE CHANNEL AND THE
UNDERGROUND WATER 256 10.1 SYSTEM OF EQUATIONS: STATEMENT OF THE PROBLEM
. . . . . . 256 10.2 LOCALIZATION EFFECTS IN THE EQUATIONS OF DIFFUSION
WAVES . .258 10.3 FINITE SPEED OF PROPAGATION FOR SIMULTANEOUS FLOWS . .
. .260 11 SOLUTE TRANSPORT THROUGH A POROUS MEDIUM WITH MICRO AND MACRO
STRUCTURES 264 12 A QUASILINEAR DEGENERATE SYSTEM ARISING IN
SEMICONDUCTOR THEORY 269 13 BLOWUP IN SOLUTIONS OF THE THERMISTOR
PROBLEM 275 13.1 THE NEUMANN BOUNDARY CONDITION FOR U(X, T) 277 13.1.1
BLOWUP DRIVEN BY 13.1.2 BLOWUP DRIVEN BY (P 280 VIII CONTENTS 13.2
MIXED BOUNDARY CONDITION FOR U{X, T) 282 13.2.1 BLOWUP DRIVEN BY 284
13.2.2 BLOWUP DRIVEN BY 286 13.3 THE DIRICHLET BOUNDARY CONDITION FOR U
288 13.3.1 GENERALIZATION TO THE CASE OF A MOVING NONHO- MOGENEOUS
INCOMPRESSIBLE MEDIUM 290 APPENDIX 293 1 THE FUNCTION SPACES 293 2
ELEMENTARY INEQUALITIES 295 2.1 ALGEBRAIC INEQUALITIES 295 2.2 INTEGRAL
INEQUALITIES 295 3 EMBEDDING THEOREMS 296 3.1 INTERPOLATION INEQUALITIES
296 3.2 ANISOTROPIC FUNCTION SPACES 299 REFERENCES 301 INDEX 325
|
| any_adam_object | 1 |
| author | Antoncev, Stanislav N. Díaz, Jesús Ildefonso 1950- Šmarev, Sergej I. 1958- |
| author_GND | (DE-588)121416283 (DE-588)123470293 (DE-588)123470331 |
| author_facet | Antoncev, Stanislav N. Díaz, Jesús Ildefonso 1950- Šmarev, Sergej I. 1958- |
| author_role | aut aut aut |
| author_sort | Antoncev, Stanislav N. |
| author_variant | s n a sn sna j i d ji jid s i š si siš |
| building | Verbundindex |
| bvnumber | BV013990012 |
| classification_rvk | SK 540 SK 950 |
| ctrlnum | (OCoLC)635065427 (DE-599)BVBBV013990012 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013990012 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:39Z |
| institution | BVB |
| isbn | 0817641238 3764341238 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009575462 |
| oclc_num | 635065427 |
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| owner | DE-824 DE-355 DE-BY-UBR DE-703 DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-824 DE-355 DE-BY-UBR DE-703 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 329 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Antoncev, Stanislav N. Verfasser (DE-588)121416283 aut Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics S. N. Antontsev ; J. I. Diaz ; S. Shmarev Boston [u.a.] Birkhäuser 2002 XI, 329 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 48 Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Energiemethode (DE-588)4152223-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Freies Randwertproblem (DE-588)4155303-2 s Strömungsmechanik (DE-588)4077970-1 s Energiemethode (DE-588)4152223-0 s DE-604 Hydrodynamik (DE-588)4026302-2 s Díaz, Jesús Ildefonso 1950- Verfasser (DE-588)123470293 aut Šmarev, Sergej I. 1958- Verfasser (DE-588)123470331 aut Progress in nonlinear differential equations and their applications 48 (DE-604)BV007934389 48 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009575462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Antoncev, Stanislav N. Díaz, Jesús Ildefonso 1950- Šmarev, Sergej I. 1958- Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics Progress in nonlinear differential equations and their applications Hydrodynamik (DE-588)4026302-2 gnd Energiemethode (DE-588)4152223-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Freies Randwertproblem (DE-588)4155303-2 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4152223-0 (DE-588)4077970-1 (DE-588)4128900-6 (DE-588)4155303-2 |
| title | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics |
| title_auth | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics |
| title_exact_search | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics |
| title_full | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics S. N. Antontsev ; J. I. Diaz ; S. Shmarev |
| title_fullStr | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics S. N. Antontsev ; J. I. Diaz ; S. Shmarev |
| title_full_unstemmed | Energy methods for free boundary problems applications to nonlinear PDEs and fluid mechanics S. N. Antontsev ; J. I. Diaz ; S. Shmarev |
| title_short | Energy methods for free boundary problems |
| title_sort | energy methods for free boundary problems applications to nonlinear pdes and fluid mechanics |
| title_sub | applications to nonlinear PDEs and fluid mechanics |
| topic | Hydrodynamik (DE-588)4026302-2 gnd Energiemethode (DE-588)4152223-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Freies Randwertproblem (DE-588)4155303-2 gnd |
| topic_facet | Hydrodynamik Energiemethode Strömungsmechanik Nichtlineare partielle Differentialgleichung Freies Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009575462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT antoncevstanislavn energymethodsforfreeboundaryproblemsapplicationstononlinearpdesandfluidmechanics AT diazjesusildefonso energymethodsforfreeboundaryproblemsapplicationstononlinearpdesandfluidmechanics AT smarevsergeji energymethodsforfreeboundaryproblemsapplicationstononlinearpdesandfluidmechanics |