Maximal regularity of the solutions for some degenerate differential equations and their applications

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Akhmetkaliyeva, RayaLuleå tekniska universitet,Matematiska vetenskaper,Department of Fundamental and Applied Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan (author)

Maximal regularity of the solutions for some degenerate differential equations and their applications

BookEnglish2018

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Luleå :Luleå University of Technology,2018
electronicrdacarrier

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LIBRIS-ID:oai:DiVA.org:ltu-68293
ISBN:9789177901006
ISBN:9789177901013
https://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-68293URI

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Language:English
Summary in:English

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Subject category:vet swepub-contenttype
Subject category:dok swepub-publicationtype

Varying forms of title

Maximal regularitet av lösningarna till några degenererade differentialekvationer och deras tillämpningar

Series

Doctoral thesis / Luleå University of Technology 1 jan 1997 → …,1402-1544

Notes

This PhD thesis deals with the study of existence and uniqueness together with coercive estimates for solutions of certain differential equations.The thesis consists of six papers (papers A, B, C, D, E and F), two appendices and an introduction, which put these papers and appendices into a more general frame and which also serves as an overview of this interesting field of mathematics.In the text below the functionsr = r(x), q = q(x), m = m(x) etc. are functions on (−∞,+∞), which are different but well defined in each paper. Paper A deals with the study of separation and approximation properties for the differential operator in the Hilbert space (here is the complex conjugate of ). A coercive estimate for the solution of the second order differential equation is obtained and its applications to spectral problems for the corresponding differential operator is demonstrated. Some sufficient conditions for the existence of the solutions of a class of nonlinear second order differential equations on the real axis are obtained.In paper B necessary and sufficient conditions for the compactness of the resolvent of the second order degenerate differential operator in is obtained. We also discuss the two-sided estimates for the radius of fredholmness of this operator.In paper C we consider the minimal closed differential operator in , where are continuously differentiable functions, and is a continuous function. In this paper we show that the operator is continuously invertible when these coefficients satisfy some suitable conditions and obtain the following estimate for : ,where is the domain of .In papers D, E, and F various differential equations of the third order of the form are studied in the space .In paper D we investigate the case when and .Moreover, in paper E the equation (0.1) is studied when . Finally, in paper F the equation (0.1) is investigated under certain additional conditions on .For these equations we establish sufficient conditions for the existence and uniqueness of the solution, and also prove an estimate of the form for the solution of equation (0.1).

Subject headings and genre

NATURVETENSKAP Matematik Matematisk analys hsv//swe
NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
Matematik
Mathematics

Added entries (persons, corporate bodies, meetings, titles ...)

Persson, Lars-Erik,ProfessorLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)larserik (thesis advisor)
Wall, Peter,ProfessorLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)wall (thesis advisor)
Ospanov, Kordan,ProfessorDepartment of Fundamental and Applied Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan (thesis advisor)
Karapetyants, Alexey Karapetyants,ProfessorInstitute of Mathematics, mechanics and computer sciences, Southern Federal University, Rostov, Ryssland (opponent)
Luleå tekniska universitetMatematiska vetenskaper (creator_code:org_t)

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