No Cover Image

E-Thesis 518 views 148 downloads

On qualitative theory of solutions to nonlinear partial differential equations. / Mikhail Surnachev

Swansea University Author: Mikhail Surnachev

Abstract

"In this work I study certain aspects of qualitative behaviour of solutions to nonlinear PDEs. The thesis consists of introduction and three parts. In the first part I study solutions of Emden-Fowler type elliptic equations in nondivergence form. In this part I establish the following results;...

Full description

Published: 2010
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42611
first_indexed 2018-08-02T18:55:07Z
last_indexed 2018-08-03T10:10:37Z
id cronfa42611
recordtype RisThesis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-08-02T16:24:29.8369989</datestamp><bib-version>v2</bib-version><id>42611</id><entry>2018-08-02</entry><title>On qualitative theory of solutions to nonlinear partial differential equations.</title><swanseaauthors><author><sid>25a867f0c2b2767d4496463c6d03728e</sid><ORCID>NULL</ORCID><firstname>Mikhail</firstname><surname>Surnachev</surname><name>Mikhail Surnachev</name><active>true</active><ethesisStudent>true</ethesisStudent></author></swanseaauthors><date>2018-08-02</date><abstract>"In this work I study certain aspects of qualitative behaviour of solutions to nonlinear PDEs. The thesis consists of introduction and three parts. In the first part I study solutions of Emden-Fowler type elliptic equations in nondivergence form. In this part I establish the following results; 1. Asymptotic representation of solutions in conical domains; 2. A priori estimates for solutions to equations with weighted absorption term; 3. Existence and nonexistence of positive solutions to equations with source term in conical domains. In the second part I study regularity properties of nonlinear degenerate parabolic equations. There are two results here: A Harnack inequality and the H51der continuity for solutions of weighted degenerate parabolic equations with a time-independent weight from a suitable Muckenhoupt class; A new proof of the Holder continuity of solutions. The third part is propedeutic. In this part I gathered some facts and simple proofs relating to the Harnack inequality for elliptic equations. Both divergent and nondivergent case are considered. The material of this chapter is not new, but it is not very easy to find it in the literature. This chapter is built entirely upon the so-called ''growth lemma" ideology (introduced by E.M. Landis)."</abstract><type>E-Thesis</type><journal/><journalNumber></journalNumber><paginationStart/><paginationEnd/><publisher/><placeOfPublication/><isbnPrint/><issnPrint/><issnElectronic/><keywords>Theoretical mathematics.</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2010</publishedYear><publishedDate>2010-12-31</publishedDate><doi/><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><apcterm/><lastEdited>2018-08-02T16:24:29.8369989</lastEdited><Created>2018-08-02T16:24:29.8369989</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Mikhail</firstname><surname>Surnachev</surname><orcid>NULL</orcid><order>1</order></author></authors><documents><document><filename>0042611-02082018162508.pdf</filename><originalFilename>10805369.pdf</originalFilename><uploaded>2018-08-02T16:25:08.1030000</uploaded><type>Output</type><contentLength>5150005</contentLength><contentType>application/pdf</contentType><version>E-Thesis</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-08-02T16:25:08.1030000</embargoDate><copyrightCorrect>false</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2018-08-02T16:24:29.8369989 v2 42611 2018-08-02 On qualitative theory of solutions to nonlinear partial differential equations. 25a867f0c2b2767d4496463c6d03728e NULL Mikhail Surnachev Mikhail Surnachev true true 2018-08-02 "In this work I study certain aspects of qualitative behaviour of solutions to nonlinear PDEs. The thesis consists of introduction and three parts. In the first part I study solutions of Emden-Fowler type elliptic equations in nondivergence form. In this part I establish the following results; 1. Asymptotic representation of solutions in conical domains; 2. A priori estimates for solutions to equations with weighted absorption term; 3. Existence and nonexistence of positive solutions to equations with source term in conical domains. In the second part I study regularity properties of nonlinear degenerate parabolic equations. There are two results here: A Harnack inequality and the H51der continuity for solutions of weighted degenerate parabolic equations with a time-independent weight from a suitable Muckenhoupt class; A new proof of the Holder continuity of solutions. The third part is propedeutic. In this part I gathered some facts and simple proofs relating to the Harnack inequality for elliptic equations. Both divergent and nondivergent case are considered. The material of this chapter is not new, but it is not very easy to find it in the literature. This chapter is built entirely upon the so-called ''growth lemma" ideology (introduced by E.M. Landis)." E-Thesis Theoretical mathematics. 31 12 2010 2010-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.8369989 2018-08-02T16:24:29.8369989 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Mikhail Surnachev NULL 1 0042611-02082018162508.pdf 10805369.pdf 2018-08-02T16:25:08.1030000 Output 5150005 application/pdf E-Thesis true 2018-08-02T16:25:08.1030000 false
title On qualitative theory of solutions to nonlinear partial differential equations.
spellingShingle On qualitative theory of solutions to nonlinear partial differential equations.
Mikhail Surnachev
title_short On qualitative theory of solutions to nonlinear partial differential equations.
title_full On qualitative theory of solutions to nonlinear partial differential equations.
title_fullStr On qualitative theory of solutions to nonlinear partial differential equations.
title_full_unstemmed On qualitative theory of solutions to nonlinear partial differential equations.
title_sort On qualitative theory of solutions to nonlinear partial differential equations.
author_id_str_mv 25a867f0c2b2767d4496463c6d03728e
author_id_fullname_str_mv 25a867f0c2b2767d4496463c6d03728e_***_Mikhail Surnachev
author Mikhail Surnachev
author2 Mikhail Surnachev
format E-Thesis
publishDate 2010
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description "In this work I study certain aspects of qualitative behaviour of solutions to nonlinear PDEs. The thesis consists of introduction and three parts. In the first part I study solutions of Emden-Fowler type elliptic equations in nondivergence form. In this part I establish the following results; 1. Asymptotic representation of solutions in conical domains; 2. A priori estimates for solutions to equations with weighted absorption term; 3. Existence and nonexistence of positive solutions to equations with source term in conical domains. In the second part I study regularity properties of nonlinear degenerate parabolic equations. There are two results here: A Harnack inequality and the H51der continuity for solutions of weighted degenerate parabolic equations with a time-independent weight from a suitable Muckenhoupt class; A new proof of the Holder continuity of solutions. The third part is propedeutic. In this part I gathered some facts and simple proofs relating to the Harnack inequality for elliptic equations. Both divergent and nondivergent case are considered. The material of this chapter is not new, but it is not very easy to find it in the literature. This chapter is built entirely upon the so-called ''growth lemma" ideology (introduced by E.M. Landis)."
published_date 2010-12-31T04:21:37Z
_version_ 1851637259425546240
score 11.089718

Similar Items