Holdings: Blow-up in nonlinear equations of mathematical physics

Blow-up in nonlinear equations of mathematical physics: theory and methods

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Main Authors:	Korpusov, Maksim Olegovič (Author), Ovchinnikov, Alexey Vital'evich (Author), Svešnikov, Aleksej G. 1924- (Author), Yushkov, Egor Vladislavovich (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2018]
Series:	De Gruyter series in nonlinear analysis and applications Volume 27
Subjects:	Nichtlineare partielle Differentialgleichung Aufblasung Mathematische Physik
Online Access:	Inhaltsverzeichnis http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110601084&searchTitles=true https://www.degruyter.com/doc/cover/9783110601084.jpg Inhaltsverzeichnis
Physical Description:	XVIII, 326 Seiten 25 cm, 724 g
ISBN:	9783110601084 3110601087

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MARC


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Record in the Search Index

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adam_text	CONTENTS INTRODUCTION* XI NOTATION * XIII LIST OF NONLINEAR EQUATIONS* XVII 1 NONLINEAR CAPACITY METHOD OF S. I. POKHOZHAEV* 1 1.1 CRITICAL EXPONENT * 1 1.2 ORDINARY DIFFERENTIAL INEQUALITIES * 3 1.3 ELLIPTIC DIFFERENTIAL INEQUALITIES * 12 1.4 PARABOLIC DIFFERENTIAL INEQUALITIES * 17 1.5 HYPERBOLIC DIFFERENTIAL INEQUALITIES * 23 1.6 BIBLIOGRAPHICAL NOTES * 28 2 METHOD OF SELF-SIMILAR SOLUTIONS OF V. A. GALAKTIONOV * 31 2.1 BASIC IDEA OF THE METHOD * 32 2.2 THREE TYPES OF SELF-SIMILAR SOLUTIONS * 38 2.3 SELF-SIMILAR S-MODE, SS = O + L* 39 2.4 SELF-SIMILAR ZVS-MODE, SS O + L * 44 2.5 SELF-SIMILAR LS-MODE, SS O + L ----- 46 2.6 BLOW-UP OF LOWER SOLUTIONS * 50 2.7 BIBLIOGRAPHICAL NOTES * 54 3 METHOD OF TEST FUNCTIONS IN COMBINATION WITH METHOD OF NONLINEAR CAPACITY * 55 3.1 POKHOZHAEVS IDENTITY 55 3.2 CLASSICAL FUJITA THEOREM * 58 3.3 KORTEWEG-DE VRIES EQUATION * 62 3.4 METHOD OF FIRST EIGENFUNCTION * 66 3.5 BIBLIOGRAPHICAL NOTES * 69 4 ENERGY METHOD OF H. A. LEVINE * 71 4.1 BLOW-UP OF SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS * 71 4.2 BLOW-UP OF SOLUTIONS OF NONLINEAR WAVE EQUATION * 89 4.3 BIBLIOGRAPHICAL NOTES * 105 5 ENERGY METHOD OF 6. TODOROVA * 107 5.1 STATEMENT OF THE PROBLEM AND LOCAL SOLVABILITY * 107 V III * CONTENTS 5.2 5.3 5.4 6 6.1 6.2 6.3 6.4 7 7.1 7.2 7.3 7.4 7.5 8 8.1 8.2 8.3 8.4 8.5 9 9.1 9.2 9.3 10 10.1 10.2 10.3 10.4 10.5 10.6 11 11.1 11.2 11.3 GLOBAL SOLVABILITY AND BLOW-UP * 114 INTEGRA-DIFFERENTIAL PROBLEM WITH NONLINEAR DAMPING* 119 BIBLIOGRAPHICAL NOTES * 130 ENERGY METHOD OF S. I. POKHOZHAEV * 131 BLOW-UP FOR PARABOLIC EQUATIONS * 131 BLOW-UP FOR HYPERBOLIC EQUATIONS * 140 CRITICAL EXPONENTS OF SEMILINEAR EQUATIONS * 146 BIBLIOGRAPHICAL NOTES * 150 ENERGY METHOD OF V. K. KALANTAROV AND 0. A. LADYZHENSKAYA * 151 BASIC LEMMA * 151 BLOW-UP FOR PARABOLIC EQUATIONS * 152 BLOW-UP FOR HYPERBOLIC EQUATIONS * 158 EXAMPLES * 160 BIBLIOGRAPHICAL NOTES * 163 ENERGY METHOD OF M. 0. KORPUSOV AND A. G. SVESHNIKOV * 165 PARABOLIC EQUATIONS WITH DOUBLE NONLINEARITIES * 165 HYPERBOLIC EQUATIONS WITH POSITIVE ENERGY * 183 PSEUDO-PARABOLIC EQUATIONS WITH DOUBLE NONLINEARITIES * 204 PSEUDO-HYPERBOLIC EQUATIONS * 225 BIBLIOGRAPHICAL NOTES * 241 NONLINEAR SCHROEDINGER EQUATION * 243 VIRIAL LAW. RESULT OF GLASSEY * 243 CRITICAL CASE. CONCEPT OF BASIC STATES * 250 BIBLIOGRAPHICAL NOTES * 259 VARIATIONAL METHOD OF L. E. PAYNE AND D. H. SATTINGER* 261 INTRODUCTION * 261 POTENTIAL WELL IN THE FUNCTIONAL SPACE * 264 SOBOLEV CONSTANT * 280 BLOW-UP OF SOLUTIONS OF HYPERBOLIC EQUATIONS * 281 BLOW-UP OF SOLUTIONS OF A PARABOLIC EQUATION * 288 BIBLIOGRAPHICAL NOTES * 290 BREAKING OF SOLUTIONS OF WAVE EQUATIONS * 291 CAMASSA-HOLM EQUATION * 291 WHITHAM EQUATION * 293 BIBLIOGRAPHICAL NOTES * 295 A AUXILIARY AND ADDITIONAL RESULTS * 297 A .L DIFFERENTIAL INEQUALITY I * 297 A.2 DIFFERENTIAL INEQUALITY II * 300 A.3 DIFFERENTIAL INEQUALITY III * 308 A.4 AUXILIARY RESULTS OF THE THEORY OF VECTOR FIELDS * 311 A.5 THEOREM ON NONEXTENDABLE SOLUTION * 313 A.6 EXAMPLES OF DISPERSION BLOW-UP IN LINEAR EQUATIONS * 313 BIBLIOGRAPHY * 319 INDEX * 325
any_adam_object	1
author	Korpusov, Maksim Olegovič Ovchinnikov, Alexey Vital'evich Svešnikov, Aleksej G. 1924- Yushkov, Egor Vladislavovich
author_GND	(DE-588)1017570582 (DE-588)1164409018 (DE-588)1012307123 (DE-588)1164409220
author_facet	Korpusov, Maksim Olegovič Ovchinnikov, Alexey Vital'evich Svešnikov, Aleksej G. 1924- Yushkov, Egor Vladislavovich
author_role	aut aut aut aut
author_sort	Korpusov, Maksim Olegovič
author_variant	m o k mo mok a v o av avo a g s ag ags e v y ev evy
building	Verbundindex
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
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dewey-sort	3515.353
dewey-tens	510 - Mathematics
discipline	Mathematik
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spelling	Korpusov, Maksim Olegovič Verfasser (DE-588)1017570582 aut Blow-up in nonlinear equations of mathematical physics theory and methods Maxim Olegovich Korpusov, Alexey Vital'evich Ovchinnikov, Alexey Gergievich Sveshnikov, and Egor Vladislavovich Yushkov Berlin ; Boston De Gruyter [2018] XVIII, 326 Seiten 25 cm, 724 g txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications Volume 27 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Aufblasung (DE-588)4139570-0 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineare partielle Differentialgleichung Aufblasung Mathematische Physik Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Aufblasung (DE-588)4139570-0 s Mathematische Physik (DE-588)4037952-8 s DE-604 Ovchinnikov, Alexey Vital'evich Verfasser (DE-588)1164409018 aut Svešnikov, Aleksej G. 1924- Verfasser (DE-588)1012307123 aut Yushkov, Egor Vladislavovich Verfasser (DE-588)1164409220 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059900-8 Erscheint auch als Online-Ausgabe, PDF 978-3-11-060207-4 De Gruyter series in nonlinear analysis and applications Volume 27 (DE-604)BV005530011 27 B:DE-101 application/pdf http://d-nb.info/1154611620/04 Inhaltsverzeichnis X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110601084&searchTitles=true X:MVB https://www.degruyter.com/doc/cover/9783110601084.jpg DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030536543&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Korpusov, Maksim Olegovič Ovchinnikov, Alexey Vital'evich Svešnikov, Aleksej G. 1924- Yushkov, Egor Vladislavovich Blow-up in nonlinear equations of mathematical physics theory and methods De Gruyter series in nonlinear analysis and applications Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Aufblasung (DE-588)4139570-0 gnd Mathematische Physik (DE-588)4037952-8 gnd
subject_GND	(DE-588)4128900-6 (DE-588)4139570-0 (DE-588)4037952-8
title	Blow-up in nonlinear equations of mathematical physics theory and methods
title_auth	Blow-up in nonlinear equations of mathematical physics theory and methods
title_exact_search	Blow-up in nonlinear equations of mathematical physics theory and methods
title_full	Blow-up in nonlinear equations of mathematical physics theory and methods Maxim Olegovich Korpusov, Alexey Vital'evich Ovchinnikov, Alexey Gergievich Sveshnikov, and Egor Vladislavovich Yushkov
title_fullStr	Blow-up in nonlinear equations of mathematical physics theory and methods Maxim Olegovich Korpusov, Alexey Vital'evich Ovchinnikov, Alexey Gergievich Sveshnikov, and Egor Vladislavovich Yushkov
title_full_unstemmed	Blow-up in nonlinear equations of mathematical physics theory and methods Maxim Olegovich Korpusov, Alexey Vital'evich Ovchinnikov, Alexey Gergievich Sveshnikov, and Egor Vladislavovich Yushkov
title_short	Blow-up in nonlinear equations of mathematical physics
title_sort	blow up in nonlinear equations of mathematical physics theory and methods
title_sub	theory and methods
topic	Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Aufblasung (DE-588)4139570-0 gnd Mathematische Physik (DE-588)4037952-8 gnd
topic_facet	Nichtlineare partielle Differentialgleichung Aufblasung Mathematische Physik
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volume_link	(DE-604)BV005530011
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