Nonlinear evolution equations, global behavior of solutions:
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Format: | Buch |
Sprache: | Undetermined |
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1981
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adam_text | TABLE OF CONTENTS
Introduction XI
A. THE CAUCHY PROBLEM 1
I. Generalities and Local Theory 1
Lecture 1: Generalities, the continuous and
linear cases 1
Lecture 2: Quasilinear evolution equations 10
II. The Global Existence Problem 19
Lecture 3: Generalities, first integrals and
Liapunov functions 19
Lecture 4: Methods relying on the Gronwall lemma .. 27
Lecture 5: A singular generalized Gronwall lemma
and application to a special nonlinear
Schrodinger problem 32
BIBLIOGRAPHY FOR CHAPTER A-1,11 38
III. Theory of Monotone Operators and Applications 39
Lecture 6: General properties, Minty s theorem,
Yoshida s regularization 40
Lecture 7: Examples of maximal montone
operators 47
Lecture 8: Sums of maximal monotone operators 54
Lecture 9: The range of a maximal monotone
operator 60
Lecture 10: Quasi-autonomous systems generated by a
maximal monotone operator 70
1. Nonlinear semi-group generated by -A 70
2. Quasi-autonomous systems 75
Lecture 11: Further properties of solutions 80
1. The relationship between weak and
strong solutions 80
2. The Benilan-Brezis characterization of
weak solutions 83
VI
Page
3. Dependence upon the operator A 85
4. Lipschitzian perturbations 86
Lecture 12: Examples of nonlinear dissipative
systems 88
1. Parabolic case 88
2. A dissipative hyperbolic system 88
BIBLIOGRAPHYFORCHAPTERA.III 94
IV. Smoothing Effect for Some Nonlinear Evolution
Equations 96
Lecture 13: Smoothing effect associated with
monotone operators 96
1. The parabolic autonomous case 96
2. The parabolic quasi-autonomous case 99
3. The finite dimensional case 104
Lecture 14: Smoothing effect for a nonmonotone
parabolic system 105
Lecture 15: Generalized solutions for a special
nonlinear Schrodinger equation Ill
BIBLIOGRAPHY FOR CHAPTER A, IV 117
V. Schrodinger and Wave Equations with a
Logarithmic Nonlinearity 118
Lecture 16: An unexpected use of the monotonicity
method 118
Lecture 17: Solutions in H for the nonlinear
logarithmic Schrodinger equation .... 126
Lecture 18: The wave equation with logarithmic
nonlinearity 137
BIBLIOGRAPHY FOR CHAPTER A,V 147
VII
Page
B. THE QUASI-AUTONOMOUS PERIODIC PROBLEM 148
I. The Linear Case: Hilbertian Theory
and Applications 148
Lecture 19: Some general results 148
Lecture 20: Examples 157
BIBLIOGRAPHY FOR CHAPTER B,I 163
II. Some Nonlinear Monotone Cases 164
Lecture 21: The parabolic monotone case 164
Lecture 22: The general monotone case and the
example of the dissipative nonlinear
wave equation 173
1. Generalities 173
2. Application to the dissipative
wave equation 176
BIBLIOGRAPHY FOR CHAPTER B,11 183
III. Some Nonlinear, Non Monotone Cases 184
Lecture 23: Some results in the non monotone
framework 184
1. A result of Mawhin-Walter for first order
order O.D.E 184
2. A second order differential equation of
elliptic type 187
3. A type of second order O.D.E 190
4. A nonlinear wave equation with periodic
forcing 192
BIBLIOGRAPHY FOR CHAPTER B,III iss
C. ASYMPTOTIC BEHAVIOR 200
I. Autonomous Dissipative Systems 200
Lecture 24: Some simple facts about almost
periodic functions 200
VIII
Page
Lecture 25: The linear dissipative case 204
0. Preliminary results 204
1. Some results in the complex framework 205
2. General results in the real framework 207
Lecture 26: The case of nonlinear
semi-groups 215
BIBLIOGRAPHY FOR CHAPTER C,I 239
II. General Results for Quasi-Autonomous Periodic
Systems 241
Lecture 27: General dissipative parabolic
systems 241
Lecture 28: A general method for non parabolic
dissipative systems 249
Lecture 29: Continuous perturbations of
dissipative linear systems 255
BIBLIOGRAPHY FOR CHAPTER C,11 265
D. MORE SPECIALIZED TOPICS 266
I. More on Asymptotic Behavior for Solutions of the
Nonlinear Dissipative Forced Wave Equation 266
Lecture 30: Case of a strictly monotone
damping 267
Lecture 31: Case of a single valued damping
term 276
BIBLIOGRAPHY FOR CHAPTER D,I 283
II. Boundedness of Trajectories for Quasi-Autonomous
Dissipative Systems 284
Lecture 32: The coercive and parabolic
cases 284
Lecture 33: A method of G. Prouse for
hyperbolic case 291
BIBLIOGRAPHY FOR CHAPTER D,II 294
IX
Page
III. Almost-Periodic Quasi-Autonomous Dissipative
Systems in a Hilbert Space 295
Lecture 34: A general result 295
Lecture 35: Application to strongly dissipative
nonlinear wave equation 301
BIBLIOGRAPHY FOR CHAPTER D,III 308
Selective Index 310
Notation Index 313
|
any_adam_object | 1 |
author | Haraux, Alain |
author_facet | Haraux, Alain |
author_role | aut |
author_sort | Haraux, Alain |
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classification_rvk | SI 850 |
contents | Berlin [u.a.]: Springer 1981. XII, 312 S.m.Abb.u.Taf. 8 (4)<br>(Lecture Notes in mathematic. 841.) |
ctrlnum | (OCoLC)720767855 (DE-599)BVBBV018136783 |
discipline | Mathematik |
format | Book |
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spelling | Haraux, Alain Verfasser aut Nonlinear evolution equations, global behavior of solutions 1981 txt rdacontent n rdamedia nc rdacarrier Berlin [u.a.]: Springer 1981. XII, 312 S.m.Abb.u.Taf. 8 (4)<br>(Lecture Notes in mathematic. 841.) Lösung Chemie (DE-588)4036159-7 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Globale Lösung (DE-588)4264389-2 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Lösung Chemie (DE-588)4036159-7 s DE-604 Evolutionsgleichung (DE-588)4129061-6 s Nichtlineares Phänomen (DE-588)4136065-5 s Globale Lösung (DE-588)4264389-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010907597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Haraux, Alain Nonlinear evolution equations, global behavior of solutions Berlin [u.a.]: Springer 1981. XII, 312 S.m.Abb.u.Taf. 8 (4)<br>(Lecture Notes in mathematic. 841.) Lösung Chemie (DE-588)4036159-7 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineares Phänomen (DE-588)4136065-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Globale Lösung (DE-588)4264389-2 gnd |
subject_GND | (DE-588)4036159-7 (DE-588)4221363-0 (DE-588)4136065-5 (DE-588)4129061-6 (DE-588)4264389-2 |
title | Nonlinear evolution equations, global behavior of solutions |
title_auth | Nonlinear evolution equations, global behavior of solutions |
title_exact_search | Nonlinear evolution equations, global behavior of solutions |
title_full | Nonlinear evolution equations, global behavior of solutions |
title_fullStr | Nonlinear evolution equations, global behavior of solutions |
title_full_unstemmed | Nonlinear evolution equations, global behavior of solutions |
title_short | Nonlinear evolution equations, global behavior of solutions |
title_sort | nonlinear evolution equations global behavior of solutions |
topic | Lösung Chemie (DE-588)4036159-7 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineares Phänomen (DE-588)4136065-5 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Globale Lösung (DE-588)4264389-2 gnd |
topic_facet | Lösung Chemie Nichtlineare Evolutionsgleichung Nichtlineares Phänomen Evolutionsgleichung Globale Lösung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010907597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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