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Dissertations / Theses on the topic 'Boundary value problems'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Cossio, Jorge Ivan. "Multiple solutions for semilinear elliptic boundary value problems." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc332487/.

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In this paper results concerning a semilinear elliptic boundary value problem are proven. This problem has five solutions when the range of the derivative of the nonlinearity ƒ includes the first two eigenvalues. The existence and multiplicity or radially symmetric solutions under suitable conditions on the nonlinearity when Ω is a ball in R^N.

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2

Zhao, Kun. "Initial-boundary value problems in fluid dynamics modeling." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31778.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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3

Mohammed, Alip. "Boundary value problems of complex variables." [S.l. : s.n.], 2002. http://www.diss.fu-berlin.de/2003/23/index.html.

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4

Rabinovich, Vladimir, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "Boundary value problems in cuspidal wedges." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2536/.

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The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.

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5

Xiaochun, Liu, and Bert-Wolfgang Schulze. "Boundary value problems in edge representation." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2674/.

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Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the ass

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6

Schulze, Bert-Wolfgang, and Nikolai Tarkhanov. "Boundary value problems with Toeplitz conditions." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2983/.

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We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.

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7

Ashton, Anthony Charles Lewis. "Nonlocal approaches to boundary value problems." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/252204.

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8

Delecki, Zdzislaw Andrzej. "Boundary value problems in dielectric spectroscopy." Thesis, University of Ottawa (Canada), 1989. http://hdl.handle.net/10393/21430.

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9

Alsaedy, Ammar, and Nikolai Tarkhanov. "Normally solvable nonlinear boundary value problems." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6507/.

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We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvabl

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10

Traytak, Sergey D. "Boundary-value problems for the diffusion equation in domains with disconnected boundary: Boundary-value problems for the diffusion equation in domainswith disconnected boundary." Diffusion fundamentals 2 (2005) 38, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14368.

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11

Roman, Svetlana. "Green's functions for boundary-value problems with nonlocal boundary conditions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111227_092148-01085.

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In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introd

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12

Dyer, Luke Oliver. "Parabolic boundary value problems with rough coefficients." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33276.

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This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a re

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13

Mugnolo, Delio. "Second order abstract initial-boundary value problems." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971647674.

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14

Schrohe, Elmar, and Bert-Wolfgang Schulze. "Edge-degenerate boundary value problems on cones." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2543/.

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We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.

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15

Rabinovich, Vladimir, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "Boundary value problems in domains with corners." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2555/.

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16

Harutyunyan, G., and Bert-Wolfgang Schulze. "Boundary value problems in weighted edge spaces." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3010/.

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We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.

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17

Schulze, Bert-Wolfgang. "Boundary value problems with the transmission property." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/3037/.

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We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.

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18

Kunkel, Curtis J. Henderson Johnny. "Positive solutions of singular boundary value problems." Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5022.

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19

Heredia, N. Fernando. "A new method for boundary value problems." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21467.

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20

Spence, Euan Alastair. "Boundary value problems for linear elliptic PDEs." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609476.

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21

Mandal, Subhas Chandra. "Some mixed boundary value problems in elastodynamics." Thesis, University of North Bengal, 1992. http://hdl.handle.net/123456789/628.

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22

Das, Apurba Narayan. "Some boundary value problems in linear elastodynamics." Thesis, University of North Bengal, 1993. http://hdl.handle.net/123456789/630.

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23

Das, Ashoke. "On some boundary and mixed boundary value problems of thermo-elasticity." Thesis, University of North Bengal, 1999. http://hdl.handle.net/123456789/634.

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24

Kreuter, Marcel [Verfasser]. "Vector-valued elliptic boundary value problems on rough domains / Marcel Kreuter." Ulm : Universität Ulm, 2019. http://d-nb.info/1177882434/34.

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25

Schulze, Bert-Wolfgang, Vladimir Nazaikinskii, Boris Sternin, and Victor Shatalov. "Spectral boundary value problems and elliptic equations on singular manifolds." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2514/.

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For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.

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26

Rutka, Vita. "Immersed interface methods for elliptic boundary value problems." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=974190918.

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27

Schulze, Bert-Wolfgang, Boris Sternin, and Victor Shatalov. "On general boundary value problems for elliptic equations." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2513/.

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We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.

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28

Schulze, Bert-Wolfgang, and Jörg Seiler. "The edge algebra structure of boundary value problems." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2595/.

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Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators w

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29

Schulze, Bert-Wolfgang, and Jörg Seiler. "Pseudodifferential boundary value problems with global projection conditions." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2623/.

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Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero

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30

Windisch, G. "Exact discretizations of two-point boundary value problems." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800804.

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In the paper we construct exact three-point discretizations of linear and nonlinear two-point boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal M-matrices in the linear case and M-functions in the nonlinear case.

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31

Garcia, Maxine Patricia. "Collocation methods for mixed order boundary value problems." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322404.

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32

Matar, Samir A. "Numerical methods for high-order boundary-value problems." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293058.

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33

Siddiqi, Shahid S. "Spline solutions of high-order boundary-value problems." Thesis, Brunel University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384827.

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34

Kassianidis, Fotios. "Boundary-value problems for transversely isotropic hyperelastic solids." Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/20/.

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In this thesis we examine three boundary-value problems combined with the presence of dead-load tractions in respect of transersely isotropic elastic materials. In particular, Chapter 1 mainly consists of existing preliminary remarks on the continuum (phenomenological) approach used here to study the mechanical response of elastic materials under large strains. More specifically, we discuss, always within the continuous framework, basic kinematical concepts, fundamental stress principles as well as balance laws; those also being appropriately specialized for material bodies under the state of

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35

Shepherd, Duncan Paul. "Theoretical fracture mechanics and elliptic boundary value problems." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243658.

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36

Kaye, Adelina E. "Singular integration with applications to boundary value problems." Kansas State University, 2016. http://hdl.handle.net/2097/32717.

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Master of Science<br>Mathematics<br>Nathan Albin<br>Pietro Poggi-Corradini<br>This report explores singular integration, both real and complex, focusing on the the Cauchy type integral, culminating in the proof of generalized Sokhotski-Plemelj formulae and the applications of such to a Riemann-Hilbert problem.

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37

Carrasco, Hugo Alexandre Sacristão. "Higher order boundary value problems on unbounded intervals." Doctoral thesis, Universidade de Évora, 2017. http://hdl.handle.net/10174/21093.

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The relative scarcity of results that guarantee the existence of solutions for BVP on unbounded domains, contrasts with the high applicability on real problems of differential equations defined on the half-line or on the whole real line. It is this gap the main reason that led to this work. The differential equations studied vary from second order to higher orders and they can be discontinuous on time. Different types of boundary conditions will be discussed herein, for example, Sturm- Liouville, homoclinic, Lidstone and functional conditions. The non-compactness of the time interval and the p

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38

Al-Kharafi, Abdulmohsen A. H. "Finite element solution of initial/boundary value problems." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/32335.

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In the last few decades, the Finite Element Method (F.E.M.) has become one of the best techniques used to solve a vast variety of the world's initial/boundary value problems. When such a powerful method is facilitated by a 'user friendly' computer program that possess both pre- and post-processors together with an automatic mesh generation and refinement processor, it becomes indeed a powerful tool to solve a wide range of problems in Applied Mathematics and Engineering. This thesis is an attempt to show the potential of the method which is implemented by a general purpose program used to solv

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39

Cameron, Seth Andrew 1967. "Novel Fourier methods for biomagnetic boundary value problems." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/278738.

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A novel Fourier technique for solving a wide variety of boundary value problems is introduced. The technique, called Fourier projection, is based on the geometric properties of vector calculus operators in reciprocal space. Fourier projection decomposes arbitrary vector fields into collections of irrotational and/or divergenceless dipole subfields. For well-posed problems, Fourier projection algorithms can calculate unknown field values from a knowledge of primary sources and boundary conditions. Specifically, this technique is applied to several problems associated with biomagnetic imaging, i

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40

Eidenschink, Michael. "A comparison of numerical methods for the solution of two-point boundary value problems." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/29224.

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41

Traytak, Sergey D. "Boundary-value problems for the diffusion equation in domains with disconnected boundary." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-195662.

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42

Bock, Hans Georg. "Randwertproblemmethoden zur Parameteridentifizierung in Systemen Nichtlinearer Differentialgleichungen." Bonn : Rheinische Friedrich-Wilhelms-Universität, 1987. http://catalog.hathitrust.org/api/volumes/oclc/16795956.html.

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43

Tisdell, Christopher C. "On the existence of solutions to discrete and continuous boundary value problems /." [St. Lucia, Qld.], 2001. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe16271.pdf.

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44

Hwang, J. S. "A discontinuity study in shielded coplanar line." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA242976.

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Thesis (M.S. in Electrical and Computer Engineering)--Naval Postgraduate School, December 1990.<br>Thesis Advisor(s): Atwater, H.A. Second Reader: Lee, H.M. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Identifier(s): Circuits, Computerized Simulation, Discontinuities, FORTRAN, SCPL(Shielded Coplanar Line), Theses, Computations, Boundary Value Problems. Author(s) subject terms: A discontinuity study in shielded coplanar line. Includes bibliographical references (p. 57). Also available in print.

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45

Kapanadze, David, and Bert-Wolfgang Schulze. "Boundary value problems on manifolds with exits to infinity." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2572/.

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We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we

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46

Oliaro, Alessandro, and Bert-Wolfgang Schulze. "Parameter-dependent boundary value problems on manifolds with edges." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2642/.

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As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conorma

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47

Krainer, Thomas, and Bert-Wolfgang Schulze. "The conormal symbolic structure of corner boundary value problems." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2666/.

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Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.

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48

Qin, Jingsheng. "Initial boundary value problems associated with a spinning string." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq23465.pdf.

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49

Khan, Mohammad Salim. "Finite-difference solutions of fifth-order boundary-value problems." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239268.

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50

Akbar, M. M. "Boundary-value problems in quantum gravity and classical solutions." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595407.

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It is proved that Taub-Bolt infillings are double-valued whereas Taub-Nut and Eguchi-Hanson infillings are unique in arbitrary dimensions. In the case of trivial bundles, there are two or no Schwarzschild infillings. The condition of whether a particular type of infilling exists can be expressed as a limitation on squashing through a functional dependence on dimension in each case. The case of the Eguchi-Hanson metric is solved in arbitrary dimension. The Taub-Nut and the Taub-Bolt are solved in four dimensions and methods for higher dimensions are discussed. For the case of Schwarzschild in a

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