Nonlinear diffusion equations /:
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biolog...
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| Format: | Elektronisch E-Book |
| Sprache: | English Chinese |
| Veröffentlicht: |
River Edge, N.J. :
World Scientific,
©2001.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. |
| Beschreibung: | 1 online resource (xvii, 502 pages) |
| Bibliographie: | Includes bibliographical references (pp479-502). |
| ISBN: | 9789812799791 9812799796 1281951358 9781281951359 9786611951351 6611951350 |
Internformat
MARC
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| 245 | 0 | 0 | |a Nonlinear diffusion equations / |c Zhuoqun Wu, Junning Zhao and Jingxue Yin, Huilai Li. |
| 260 | |a River Edge, N.J. : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xvii, 502 pages) | ||
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| 504 | |a Includes bibliographical references (pp479-502). | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. | ||
| 505 | 0 | |a Ch. 1. Newtonian filtration equations. 1.1. Introduction. 1.2. Existence and uniqueness of solutions: One dimensional case. 1.3. Existence and uniqueness of solutions: Higher dimensional case. 1.4. Regularity of solutions: One Dimensional case. 1.5. Regularity of solutions: Higher dimensional case. 1.6. Properties of the free boundary: One dimensional case. 1.7. Properties of the free boundary: Higher dimensional case. 1.8. Initial trace of solutions. 1.9. Other problems -- ch. 2. Non-Newtonian filtration equations. 2.1. Introduction. Preliminary knowledge. 2.2. Existence of solutions. 2.3. Harnack inequality and the initial trace of solutions. 2.4. Regularity of solutions. 2.5. Uniqueness of solutions. 2.6. Properties of the free boundary. 2.7. Other problems -- ch. 3. General quasilinear equations of second order. 3.1. Introduction. 3.2. Weakly degenerate equations in one dimension. 3.3. Weakly Degenerate equations in higher dimension. 3.4. Strongly degenerate equations in one dimension. 3.5. Degenerate equations in higher dimension without terms of lower order. 3.6. General strongly degenerate equations in higher dimension -- ch. 4. Nonlinear diffusion equations of higher order. 4.1. Introduction. 4.2. Similarity solutions of a fourth order equation. 4.3. Equations with double-degeneracy. 4.4. Cahn-Hilliard equation with constant mobility. 4.5. Cahn-Hilliard equations with positive concentration dependent mobility. 4.6. Thin film equation. 4.7. Cahn-Hilliard equation with degenerate mobility. | |
| 546 | |a English. | ||
| 650 | 0 | |a Burgers equation. |0 http://id.loc.gov/authorities/subjects/sh85018060 | |
| 650 | 0 | |a Heat equation. |0 http://id.loc.gov/authorities/subjects/sh85059782 | |
| 650 | 6 | |a Équation de Burgers. | |
| 650 | 6 | |a Équation de la chaleur. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Ordinary. |2 bisacsh | |
| 650 | 7 | |a Burgers equation |2 fast | |
| 650 | 7 | |a Heat equation |2 fast | |
| 700 | 1 | |a Wu, Zhuoqun. | |
| 758 | |i has work: |a Nonlinear diffusion equations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGc4JYPcg7VbK4RGmjTBmq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Nonlinear diffusion equations. |d River Edge, N.J. : World Scientific, ©2001 |w (DLC) 2002265584 |
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Datensatz im Suchindex
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| _version_ | 1816881725107601408 |
| adam_text | |
| any_adam_object | |
| author2 | Wu, Zhuoqun |
| author2_role | |
| author2_variant | z w zw |
| author_facet | Wu, Zhuoqun |
| author_sort | Wu, Zhuoqun |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 .N653 2001eb |
| callnumber-search | QA372 .N653 2001eb |
| callnumber-sort | QA 3372 N653 42001EB |
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| collection | ZDB-4-EBA |
| contents | Ch. 1. Newtonian filtration equations. 1.1. Introduction. 1.2. Existence and uniqueness of solutions: One dimensional case. 1.3. Existence and uniqueness of solutions: Higher dimensional case. 1.4. Regularity of solutions: One Dimensional case. 1.5. Regularity of solutions: Higher dimensional case. 1.6. Properties of the free boundary: One dimensional case. 1.7. Properties of the free boundary: Higher dimensional case. 1.8. Initial trace of solutions. 1.9. Other problems -- ch. 2. Non-Newtonian filtration equations. 2.1. Introduction. Preliminary knowledge. 2.2. Existence of solutions. 2.3. Harnack inequality and the initial trace of solutions. 2.4. Regularity of solutions. 2.5. Uniqueness of solutions. 2.6. Properties of the free boundary. 2.7. Other problems -- ch. 3. General quasilinear equations of second order. 3.1. Introduction. 3.2. Weakly degenerate equations in one dimension. 3.3. Weakly Degenerate equations in higher dimension. 3.4. Strongly degenerate equations in one dimension. 3.5. Degenerate equations in higher dimension without terms of lower order. 3.6. General strongly degenerate equations in higher dimension -- ch. 4. Nonlinear diffusion equations of higher order. 4.1. Introduction. 4.2. Similarity solutions of a fourth order equation. 4.3. Equations with double-degeneracy. 4.4. Cahn-Hilliard equation with constant mobility. 4.5. Cahn-Hilliard equations with positive concentration dependent mobility. 4.6. Thin film equation. 4.7. Cahn-Hilliard equation with degenerate mobility. |
| ctrlnum | (OCoLC)646768325 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Newtonian filtration equations. 1.1. Introduction. 1.2. Existence and uniqueness of solutions: One dimensional case. 1.3. Existence and uniqueness of solutions: Higher dimensional case. 1.4. 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| id | ZDB-4-EBA-ocn646768325 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:17:17Z |
| institution | BVB |
| isbn | 9789812799791 9812799796 1281951358 9781281951359 9786611951351 6611951350 |
| language | English Chinese |
| oclc_num | 646768325 |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Nonlinear diffusion equations / Zhuoqun Wu, Junning Zhao and Jingxue Yin, Huilai Li. River Edge, N.J. : World Scientific, ©2001. 1 online resource (xvii, 502 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pp479-502). Print version record. Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. Ch. 1. Newtonian filtration equations. 1.1. Introduction. 1.2. Existence and uniqueness of solutions: One dimensional case. 1.3. Existence and uniqueness of solutions: Higher dimensional case. 1.4. Regularity of solutions: One Dimensional case. 1.5. Regularity of solutions: Higher dimensional case. 1.6. Properties of the free boundary: One dimensional case. 1.7. Properties of the free boundary: Higher dimensional case. 1.8. Initial trace of solutions. 1.9. Other problems -- ch. 2. Non-Newtonian filtration equations. 2.1. Introduction. Preliminary knowledge. 2.2. Existence of solutions. 2.3. Harnack inequality and the initial trace of solutions. 2.4. Regularity of solutions. 2.5. Uniqueness of solutions. 2.6. Properties of the free boundary. 2.7. Other problems -- ch. 3. General quasilinear equations of second order. 3.1. Introduction. 3.2. Weakly degenerate equations in one dimension. 3.3. Weakly Degenerate equations in higher dimension. 3.4. Strongly degenerate equations in one dimension. 3.5. Degenerate equations in higher dimension without terms of lower order. 3.6. General strongly degenerate equations in higher dimension -- ch. 4. Nonlinear diffusion equations of higher order. 4.1. Introduction. 4.2. Similarity solutions of a fourth order equation. 4.3. Equations with double-degeneracy. 4.4. Cahn-Hilliard equation with constant mobility. 4.5. Cahn-Hilliard equations with positive concentration dependent mobility. 4.6. Thin film equation. 4.7. Cahn-Hilliard equation with degenerate mobility. English. Burgers equation. http://id.loc.gov/authorities/subjects/sh85018060 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Équation de Burgers. Équation de la chaleur. MATHEMATICS Differential Equations Ordinary. bisacsh Burgers equation fast Heat equation fast Wu, Zhuoqun. has work: Nonlinear diffusion equations (Text) https://id.oclc.org/worldcat/entity/E39PCGc4JYPcg7VbK4RGmjTBmq https://id.oclc.org/worldcat/ontology/hasWork Print version: Nonlinear diffusion equations. River Edge, N.J. : World Scientific, ©2001 (DLC) 2002265584 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235784 Volltext |
| spellingShingle | Nonlinear diffusion equations / Ch. 1. Newtonian filtration equations. 1.1. Introduction. 1.2. Existence and uniqueness of solutions: One dimensional case. 1.3. Existence and uniqueness of solutions: Higher dimensional case. 1.4. Regularity of solutions: One Dimensional case. 1.5. Regularity of solutions: Higher dimensional case. 1.6. Properties of the free boundary: One dimensional case. 1.7. Properties of the free boundary: Higher dimensional case. 1.8. Initial trace of solutions. 1.9. Other problems -- ch. 2. Non-Newtonian filtration equations. 2.1. Introduction. Preliminary knowledge. 2.2. Existence of solutions. 2.3. Harnack inequality and the initial trace of solutions. 2.4. Regularity of solutions. 2.5. Uniqueness of solutions. 2.6. Properties of the free boundary. 2.7. Other problems -- ch. 3. General quasilinear equations of second order. 3.1. Introduction. 3.2. Weakly degenerate equations in one dimension. 3.3. Weakly Degenerate equations in higher dimension. 3.4. Strongly degenerate equations in one dimension. 3.5. Degenerate equations in higher dimension without terms of lower order. 3.6. General strongly degenerate equations in higher dimension -- ch. 4. Nonlinear diffusion equations of higher order. 4.1. Introduction. 4.2. Similarity solutions of a fourth order equation. 4.3. Equations with double-degeneracy. 4.4. Cahn-Hilliard equation with constant mobility. 4.5. Cahn-Hilliard equations with positive concentration dependent mobility. 4.6. Thin film equation. 4.7. Cahn-Hilliard equation with degenerate mobility. Burgers equation. http://id.loc.gov/authorities/subjects/sh85018060 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Équation de Burgers. Équation de la chaleur. MATHEMATICS Differential Equations Ordinary. bisacsh Burgers equation fast Heat equation fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85018060 http://id.loc.gov/authorities/subjects/sh85059782 |
| title | Nonlinear diffusion equations / |
| title_auth | Nonlinear diffusion equations / |
| title_exact_search | Nonlinear diffusion equations / |
| title_full | Nonlinear diffusion equations / Zhuoqun Wu, Junning Zhao and Jingxue Yin, Huilai Li. |
| title_fullStr | Nonlinear diffusion equations / Zhuoqun Wu, Junning Zhao and Jingxue Yin, Huilai Li. |
| title_full_unstemmed | Nonlinear diffusion equations / Zhuoqun Wu, Junning Zhao and Jingxue Yin, Huilai Li. |
| title_short | Nonlinear diffusion equations / |
| title_sort | nonlinear diffusion equations |
| topic | Burgers equation. http://id.loc.gov/authorities/subjects/sh85018060 Heat equation. http://id.loc.gov/authorities/subjects/sh85059782 Équation de Burgers. Équation de la chaleur. MATHEMATICS Differential Equations Ordinary. bisacsh Burgers equation fast Heat equation fast |
| topic_facet | Burgers equation. Heat equation. Équation de Burgers. Équation de la chaleur. MATHEMATICS Differential Equations Ordinary. Burgers equation Heat equation |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235784 |
| work_keys_str_mv | AT wuzhuoqun nonlineardiffusionequations |