Analytic semigroups and optimal regularity in parabolic problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1995
|
| Series: | Progress in nonlinear differential equations and their applications
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVII, 424 S. |
| ISBN: | 3764351721 0817651721 9783034805568 |
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MARC
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| 100 | 1 | |a Lunardi, Alessandra |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytic semigroups and optimal regularity in parabolic problems |c Alessandra Lunardi |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1995 | |
| 300 | |a XVII, 424 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 16 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 7 | |a Semigroepen |2 gtt | |
| 650 | 7 | |a Semigroupes |2 ram | |
| 650 | 4 | |a Differential equations, Parabolic | |
| 650 | 4 | |a Semigroups | |
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Record in the Search Index
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| adam_text | Contents
Introduction IX
0 Preliminary material: spaces of continuous and
Holder continuous functions
0.1 Spaces of bounded and/or continuous functions 1
0.2 Spaces of Holder continuous functions 3
0.3 Extension operators 8
1 Interpolation theory
1.1 Interpolatory inclusions 12
1.2 Interpolation spaces 15
1.2.1 The if method 15
1.2.2 The trace method 20
1.2.3 The Reiteration Theorem 25
1.2.4 Some examples 28
1.3 Bibliographical remarks 32
2 Analytic semigroups and intermediate spaces
2.1 Basic properties of etA 35
2.1.1 Identification of the generator 40
2.1.2 A sufficient condition to be a sectorial operator 43
2.2 Intermediate spaces 44
2.2.1 The spaces DA(a,p) and DA{a) 45
2.2.2 The domains of fractional powers of —A 54
2.3 Spectral properties and asymptotic behavior 56
2.3.1 Estimates for large t 56
2.3.2 Spectral properties of etA 60
2.4 Perturbations of generators 64
2.5 Bibliographical remarks 67
V
VI Contents
3 Generation of analytic semigroups by elliptic operators
3.1 Second order operators 70
3.1.1 Generation in Lp(tt), 1 p oo 72
3.1.2 Generation in L°°(Rn) and in spaces of continuous
functions in Rn 76
3.1.3 Characterization of interpolation spaces and generation
results in Holder spaces in Rn 84
3.1.4 Generation in Cl{Rn) 90
3.1.5 Generation in L°°{Vt) and in spaces of continuous functions
in H 94
3.2 Higher order operators and bibliographical remarks 112
4 Nonhomogeneous equations
4.1 Solutions of linear problems 123
4.2 Mild solutions 129
4.3 Strict and classical solutions, and optimal regularity 133
4.3.1 Time regularity 133
4.3.2 Space regularity 142
4.3.3 A further regularity result 150
4.4 The nonhomogeneous problem in unbounded time intervals .... 153
4.4.1 Bounded solutions in [0,+oo[ 153
4.4.2 Bounded solutions in ] oo,0] 160
4.4.3 Bounded solutions in R 164
4.4.4 Exponentially decaying and exponentially growing
solutions 168
4.5 Bibliographical remarks 170
5 Linear parabolic problems
5.1 Second order equations 175
5.1.1 Initial value problems in [0, T] x Rn 178
5.1.2 Initial boundary value problems in [O,Tj x Q 192
5.2 Bibliographical remarks 208
6 Linear nonautonomous equations
6.1 Construction and properties of the evolution operator 212
6.2 The variation of constants formula 228
6.3 Asymptotic behavior in the periodic case 234
6.3.1 The period map 234
6.3.2 Estimates on the evolution operator 236
6.3.3 Asymptotic behavior in nonhomogeneous problems 240
6.4 Bibliographical remarks 250
Contents VII
7 Semilinear equations
7.1 Local existence and regularity 257
7.1.1 Local existence results 257
7.1.2 The maximally defined solution 265
7.1.3 Further regularity, classical and strict solutions ....... 268
7.2 A priori estimates and existence in the large 271
7.3 Some examples 275
7.3.1 Reaction diffusion systems 275
7.3.2 A general semilinear equation 278
7.3.3 Second order equations with nonlinearities in
divergence form 283
7.3.4 The Cahn Hilliard equation 284
7.4 Bibliographical remarks for Chapter 7 286
8 Fully nonlinear equations
8.1 Local existence, uniqueness and regularity 290
8.2 The maximally defined solution 298
8.3 Further regularity properties and dependence on the data ..... 301
8.3.1 Ck regularity with respect to (x, A) 302
8.3.2 Cfc regularity with respect to time 306
8.3.3 Analyticity 308
8.4 The case where X is an interpolation space 309
8.5 Examples and applications 313
8.5.1 An equation from detonation theory 313
8.5.2 An example of existence in the large 315
8.5.3 A general second order problem 319
8.5.4 Motion of hypersurfaces by mean curvature 329
8.5.5 Bellman equations 332
8.6 Bibliographical remarks 334
9 Asymptotic behavior in fully nonlinear equations
9.1 Behavior near stationary solutions 340
9.1.1 Stability and instability by linearization 341
9.1.2 The saddle point property 345
9.1.3 The case where X is an interpolation space 347
9.1.4 Bifurcation of stationary solutions 350
9.1.5 Applications to nonlinear parabolic problems, I ....... 355
9.1.6 Stability of travelling waves in two phase free
boundary problems 358
VIII Contents
9.2 Critical cases of stability 363
9.2.1 The center unstable manifold 363
9.2.2 Applications to nonlinear parabolic problems, II 371
9.2.3 The case where the linear part generates a bounded
semigroup 373
9.2.4 Applications to nonlinear parabolic problems, III 375
9.3 Periodic solutions 378
9.3.1 Hopf bifurcation 379
9.3.2 Stability of periodic solutions 387
9.3.3 Applications to nonlinear parabolic problems, IV 397
9.4 Bibliographical remarks 398
Appendix: Spectrum and resolvent 399
A.I Spectral sets and projections 402
A.2 Isolated points of the spectrum 404
A.3 Perturbation results 408
Bibliography 411
Index 423
|
| any_adam_object | 1 |
| author | Lunardi, Alessandra |
| author_facet | Lunardi, Alessandra |
| author_role | aut |
| author_sort | Lunardi, Alessandra |
| author_variant | a l al |
| building | Verbundindex |
| bvnumber | BV009965664 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 SK 620 |
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| ctrlnum | (OCoLC)31783118 (DE-599)BVBBV009965664 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009965664 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:44:05Z |
| institution | BVB |
| isbn | 3764351721 0817651721 9783034805568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006605169 |
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| physical | XVII, 424 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Lunardi, Alessandra Verfasser aut Analytic semigroups and optimal regularity in parabolic problems Alessandra Lunardi Basel u.a. Birkhäuser 1995 XVII, 424 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 16 Hier auch später erschienene, unveränderte Nachdrucke Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Semigroepen gtt Semigroupes ram Differential equations, Parabolic Semigroups Parabolisches System (DE-588)4352365-1 gnd rswk-swf Analytische Halbgruppe (DE-588)4376792-8 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 s DE-604 Parabolisches System (DE-588)4352365-1 s Banach-Raum (DE-588)4004402-6 s Regularität (DE-588)4049074-9 s Analytische Halbgruppe (DE-588)4376792-8 s Progress in nonlinear differential equations and their applications 16 (DE-604)BV007934389 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lunardi, Alessandra Analytic semigroups and optimal regularity in parabolic problems Progress in nonlinear differential equations and their applications Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Semigroepen gtt Semigroupes ram Differential equations, Parabolic Semigroups Parabolisches System (DE-588)4352365-1 gnd Analytische Halbgruppe (DE-588)4376792-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Regularität (DE-588)4049074-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4352365-1 (DE-588)4376792-8 (DE-588)4173245-5 (DE-588)4049074-9 (DE-588)4004402-6 |
| title | Analytic semigroups and optimal regularity in parabolic problems |
| title_auth | Analytic semigroups and optimal regularity in parabolic problems |
| title_exact_search | Analytic semigroups and optimal regularity in parabolic problems |
| title_full | Analytic semigroups and optimal regularity in parabolic problems Alessandra Lunardi |
| title_fullStr | Analytic semigroups and optimal regularity in parabolic problems Alessandra Lunardi |
| title_full_unstemmed | Analytic semigroups and optimal regularity in parabolic problems Alessandra Lunardi |
| title_short | Analytic semigroups and optimal regularity in parabolic problems |
| title_sort | analytic semigroups and optimal regularity in parabolic problems |
| topic | Equations différentielles paraboliques ram Parabolische differentiaalvergelijkingen gtt Semigroepen gtt Semigroupes ram Differential equations, Parabolic Semigroups Parabolisches System (DE-588)4352365-1 gnd Analytische Halbgruppe (DE-588)4376792-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Regularität (DE-588)4049074-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Equations différentielles paraboliques Parabolische differentiaalvergelijkingen Semigroepen Semigroupes Differential equations, Parabolic Semigroups Parabolisches System Analytische Halbgruppe Parabolische Differentialgleichung Regularität Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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