Blow-up in quasilinear parabolic equations:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
1995
|
| Series: | De Gruyter expositions in mathematics
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 533 S. graph. Darst. |
| ISBN: | 3110127547 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV009990224 | ||
| 003 | DE-604 | ||
| 005 | 20220214 | ||
| 007 | t| | ||
| 008 | 950109s1995 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 943127947 |2 DE-101 | |
| 020 | |a 3110127547 |9 3-11-012754-7 | ||
| 035 | |a (OCoLC)246790225 | ||
| 035 | |a (DE-599)BVBBV009990224 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-29T |a DE-739 |a DE-91G |a DE-12 |a DE-20 |a DE-11 |a DE-188 |a DE-19 | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a MAT 356f |2 stub | ||
| 130 | 0 | |a Režimy s obostreniem v zadačach dlja kvazilinejnych paraboličeskich uravnenij | |
| 245 | 1 | 0 | |a Blow-up in quasilinear parabolic equations |c by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld |
| 246 | 1 | 3 | |a Blow-up in quasilinear parabolic equations |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 1995 | |
| 300 | |a XXI, 533 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 19 | |
| 650 | 4 | |a Quasilineare parabolische Differentialgleichung | |
| 650 | 0 | 7 | |a Quasilineare parabolische Differentialgleichung |0 (DE-588)4253347-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quasilineare parabolische Differentialgleichung |0 (DE-588)4253347-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Samarskij, Aleksandr A. |d 1919-2008 |e Sonstige |0 (DE-588)107587351 |4 oth | |
| 700 | 1 | |a Grinfeld, Michael |d 19XX- |e Sonstige |0 (DE-588)1079849955 |4 oth | |
| 830 | 0 | |a De Gruyter expositions in mathematics |v 19 |w (DE-604)BV004069300 |9 19 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006621690 | |
Record in the Search Index
| _version_ | 1826400932872585216 |
|---|---|
| adam_text |
Contents
Introduction xi
Chapter I
Preliminary facts of the theory of second order quasilinear parabolic
equations 1
§ 1 Statement of the main problems. Comparison theorems 1
§ 2 Existence, uniqueness, and boundedness of the classical solution . 6
§ 3 Generalized solutions of quasilinear degenerate parabolic equations . . 14
Remarks and comments on the literature 35
Chapter II
Some quasilinear parabolic equations. Self similar solutions and their
asymptotic stability 38
§ 1 A boundary value problem in a half space for the heat equation. The
concept of asymptotic stability of self similar solutions 39
§ 2 Asymptotic stability of the fundamental solution of the Cauchy problem 47
§ 3 Asymptotic stability of self similar solutions of nonlinear heat equations 53
§ 4 Quasilinear heat equation in a bounded domain 61
§ 5 The fast diffusion equation. Boundary value problems in a bounded
domain 67
§ 6 The Cauchy problem for the fast diffusion equation 68
§ 7 Conditions of equivalence of different quasilinear heat equations . 74
§ 8 A heat equation with a gradient nonlinearity 84
§ 9 The Kolmogorov Petrovskii Piskunov problem 87
§ 10 Self similar solutions of the semilinear parabolic equation
u, = Am + u In u 93
§ 11 A nonlinear heat equation with a source and a sink 99
§ 12 Localization and total extinction phenomena in media with a sink . . . 101
§ 13 The structure of attractor of the semilinear parabolic equation with
absorption in R^ 107
Remarks and comments on the literature 124
viii Contents
Chapter III
Heat localization (inertia) 130
§ 1 The concept of heat localization 130
§ 2 Blowing up self similar solutions 135
§ 3 Heat "inertia" in media with nonlinear thermal conductivity 142
§ 4 Effective heat localization 158
Remarks and comments on the literature 174
Chapter IV
Nonlinear equation with a source. Blow up regimes. Localization.
Asymptotic behaviour of solutions 176
§ 1 Three types of self similar blow up regimes in combustion 178
§ 2 Asymptotic behaviour of unbounded solutions. Qualitative theory of
non stationary averaging 200
§ 3 Conditions for finite time blow up. Globally existing solutions for
P a + 1 + 2/N : 214
§ 4 Proof of localization of unbounded solutions for yS x + 1; absence
of localization in the case 1 /? r + 1 238
§ 5 Asymptotic stability of unbounded self similar solutions 257
§ 6 Asymptotics of unbounded solutions of LS regime in a neighbourhood
of the singular point 268
§ 7 Blow up regimes, effective localization for semilinear equations with
a source 274
Remarks and comments on the literature 306
Open problems 314
Chapter V
Methods of generalized comparison of solutions of different nonlinear
parabolic equations and their applications 316
§ 1 Criticality conditions and a direct solutions comparison theorem . 316
§ 2 The operator (functional) comparison method for solutions of parabolic
equations 324
§ 3 ^A criticality conditions 331
§ 4 Heat localization in problems for arbitrary parabolic nonlinear heat
equations 335
§ 5 Conditions for absence of heat localization 348
§ 6 Some approaches to the determination of conditions for unboundedness
of solutions of quasilinear parabolic equations 353
§ 7 Criticality conditions and a comparison theorem for finite difference
solutions of nonlinear heat equations 365
Remarks and comments on the literature 371
Contents ix
Chapter VI
Approximate self similar solutions of nonlinear heat equations and their
applications in the study of the localization effect 373
§ 1 Introduction. Main directions of inquiry 373
§ 2 Approximate self similar solutions in the degenerate case 375
§ 3 Approximate self similar solutions in the non degenerate case.
Pointwise estimates of the rate of convergence 386
§ 4 Approximate self similar solutions in the non degenerate case. Integral
estimates of the rate of convergence 398
Remarks and comments on the literature 413
Open problems 413
Chapter VII
Some other methods of study of unbounded solutions 414
§ 1 Method of stationary states for quasilinear parabolic equations 414
§ 2 Boundary value problems in bounded domains 430
§ 3 A parabolic system of quasilinear equations with a source 447
§ 4 The combustion localization phenomenon in multi component media . 467
§ 5 Finite difference schemes for quasilinear parabolic equations admitting
finite time blow up 476
Remarks and comments on the literature 502
Open problems 505
Bibliography 506
Index 535 |
| any_adam_object | 1 |
| author_GND | (DE-588)107587351 (DE-588)1079849955 |
| building | Verbundindex |
| bvnumber | BV009990224 |
| classification_rvk | SK 560 |
| classification_tum | MAT 356f |
| ctrlnum | (OCoLC)246790225 (DE-599)BVBBV009990224 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV009990224</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220214</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">950109s1995 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">943127947</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110127547</subfield><subfield code="9">3-11-012754-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246790225</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009990224</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 356f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="130" ind1="0" ind2=" "><subfield code="a">Režimy s obostreniem v zadačach dlja kvazilinejnych paraboličeskich uravnenij</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Blow-up in quasilinear parabolic equations</subfield><subfield code="c">by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Blow-up in quasilinear parabolic equations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">de Gruyter</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXI, 533 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter expositions in mathematics</subfield><subfield code="v">19</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quasilineare parabolische Differentialgleichung</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quasilineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4253347-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quasilineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4253347-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Samarskij, Aleksandr A.</subfield><subfield code="d">1919-2008</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)107587351</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Grinfeld, Michael</subfield><subfield code="d">19XX-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1079849955</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter expositions in mathematics</subfield><subfield code="v">19</subfield><subfield code="w">(DE-604)BV004069300</subfield><subfield code="9">19</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006621690</subfield></datafield></record></collection> |
| id | DE-604.BV009990224 |
| illustrated | Illustrated |
| indexdate | 2025-03-12T15:01:00Z |
| institution | BVB |
| isbn | 3110127547 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006621690 |
| oclc_num | 246790225 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-739 DE-91G DE-BY-TUM DE-12 DE-20 DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-29T DE-739 DE-91G DE-BY-TUM DE-12 DE-20 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XXI, 533 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Režimy s obostreniem v zadačach dlja kvazilinejnych paraboličeskich uravnenij Blow-up in quasilinear parabolic equations by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld Blow-up in quasilinear parabolic equations Berlin [u.a.] de Gruyter 1995 XXI, 533 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 19 Quasilineare parabolische Differentialgleichung Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd rswk-swf Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 s DE-604 Samarskij, Aleksandr A. 1919-2008 Sonstige (DE-588)107587351 oth Grinfeld, Michael 19XX- Sonstige (DE-588)1079849955 oth De Gruyter expositions in mathematics 19 (DE-604)BV004069300 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blow-up in quasilinear parabolic equations De Gruyter expositions in mathematics Quasilineare parabolische Differentialgleichung Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd |
| subject_GND | (DE-588)4253347-8 |
| title | Blow-up in quasilinear parabolic equations |
| title_alt | Režimy s obostreniem v zadačach dlja kvazilinejnych paraboličeskich uravnenij Blow-up in quasilinear parabolic equations |
| title_auth | Blow-up in quasilinear parabolic equations |
| title_exact_search | Blow-up in quasilinear parabolic equations |
| title_full | Blow-up in quasilinear parabolic equations by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld |
| title_fullStr | Blow-up in quasilinear parabolic equations by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld |
| title_full_unstemmed | Blow-up in quasilinear parabolic equations by Alexander A. Samarskii ... Transl. from the Russian by Michael Grinfeld |
| title_short | Blow-up in quasilinear parabolic equations |
| title_sort | blow up in quasilinear parabolic equations |
| topic | Quasilineare parabolische Differentialgleichung Quasilineare parabolische Differentialgleichung (DE-588)4253347-8 gnd |
| topic_facet | Quasilineare parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006621690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | UT rezimysobostreniemvzadacachdljakvazilinejnychparaboliceskichuravnenij AT samarskijaleksandra blowupinquasilinearparabolicequations AT grinfeldmichael blowupinquasilinearparabolicequations |