Lau Kin Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 1.1 --- Heat conduction problem --- p.3 / Chapter 1.2 --- Direct problem --- p.4 / Chapter 1.3 --- Inverse problem --- p.4 / Chapter 1.4 --- Difficulty of the inverse problems --- p.5 / Chapter 1.5 --- A simple but important example for instability --- p.5 / Chapter 1.6 --- The purpose of this thesis --- p.7 / Chapter 2 --- Stability of the inverse problem --- p.9 / Chapter 2.1 --- Conditional stability results --- p.9 / Chapter 2.2 --- Stability of the inverse problems --- p.11 / Chapter 3 --- The continuous formulation --- p.30 / Chapter 3.1 --- Constrained minimization problem --- p.30 / Chapter 3.2 --- Existence of minimizers to the minimization problem --- p.31 / Chapter 4 --- Discretization and its convergence --- p.36 / Chapter 4.1 --- Finite element space --- p.36 / Chapter 4.2 --- Two important discrete projection operators --- p.37 / Chapter 4.3 --- Finite element problem --- p.39 / Chapter 4.4 --- Existence of minimizers to the finite element problem --- p.39 / Chapter 4.5 --- Discrete minimizers and global minimizers --- p.42 / Chapter 5 --- Numerical algorithms --- p.51 / Chapter 5.1 --- Gateaux derivative --- p.51 / Chapter 5.2 --- Nonlinear single-grid gradient method --- p.53 / Chapter 5.3 --- Nonlinear multigrid gradient method --- p.55 / Chapter 6 --- Numerical experiments --- p.60 / Chapter 6.1 --- One dimensional examples --- p.60 / Chapter 6.2 --- Two dimensional examples --- p.66

Xie Jian Li. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 106-109). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Este trabalho que envolve matemática aplicada e processamento paralelo: seu objetivo é avaliar uma estratégia de implementação em paralelo para algoritmos de diferenças finitas que aproximam a solução de equações diferenciais de evolução. A alternativa proposta é a substituição dos produtos matriz-vetor efetuados sequencialmente por multiplicações matriz-matriz aceleradas pelo método de Strassen em paralelo. O trabalho desenvolve testes visando verificar o ganho computacional relacionado a essa estratégia de paralelização, pois as aplicacações computacionais, que empregam a estratégia sequencial, possuem como característica o longo período de computação causado pelo grande volume de cálculo. Inclusive como alternativa, nós usamos o algoritmo em paralelo convencional para solução de algoritmos explícitos para solução de equações diferenciais parciais evolutivas no tempo. Portanto, de acordo com os resultados obtidos, nós observamos as características de cada estratégia em paralelo, tendo como principal objetivo diminuir o esforço computacional despendido. / This work involves parallel processing and applied mathematics: Our goal is to evaluate a strategy for implementing parallel algorithms for finite diference approach,it is the solution of diferential equations of evolution. The alternative proposed is the replacement of the matrix-vector products performed sequentially by matrix-matrix multiplication method accelerated by Strassen in parallel. The work develops tests in order to verify the speedup related to the strategy of parallelization because sequential application have characterized for long periods of computation, this is caused by the large amount of calculation. Even alternatively, we use the algorithm in parallel to conventional explicit solution algorithms for solving partial diferential equations. Therefore, according to the results, we observe the characteristics of each strategy in parallel with the main purpose of reducing the computational effort expended.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-13T17:22:58Z No. of bitstreams: 1 WashingtonMenezes.pdf: 349401 bytes, checksum: 40e24e24fcc72911a8a30e2a9d7b0f1b (MD5) / Made available in DSpace on 2017-06-13T17:22:58Z (GMT). No. of bitstreams: 1 WashingtonMenezes.pdf: 349401 bytes, checksum: 40e24e24fcc72911a8a30e2a9d7b0f1b (MD5) Previous issue date: 2016-08-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this work, we introduce results of local and global solution for a heat equation in RN with nonlocal nonlinearity in time. / Neste trabalho, apresentamos resultados de existência local e global para uma equação do calor em RN com não-linearidade não local no tempo.

The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.

In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates. / Thesis (M.Sc.)-University of Natal, 1994.

We study heat transfer in one dimension with and without convection, also called advection-diffusion. This is done using the Finite Element Method (FEM) to discretise the mathematical model, i.e. the heat equation. The results are compared to analytic Fourier series solutions. Our main result is that the FEM could be used to better model the heat transfer which allow for more accurate models than today's use of steady state models.

Submitted by MARCO ANTONIO MOYA ROSAS null (23689400813) on 2016-06-08T23:48:22Z No. of bitstreams: 1 Marco.pdf: 3930307 bytes, checksum: fa27a7c6ffca34b6c67e9ba1944a88be (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-06-13T14:55:05Z (GMT) No. of bitstreams: 1 rosas_mm_me_rcla.pdf: 3930307 bytes, checksum: fa27a7c6ffca34b6c67e9ba1944a88be (MD5) / Made available in DSpace on 2016-06-13T14:55:05Z (GMT). No. of bitstreams: 1 rosas_mm_me_rcla.pdf: 3930307 bytes, checksum: fa27a7c6ffca34b6c67e9ba1944a88be (MD5) Previous issue date: 2016-04-28 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho, analisaremos o problema de boa colocação do problema de valor inicial para a equação semilinear do calor. Mostraremos a existência de solução global mild, quando o dado inicial u_0 pertence ao espaço L^( n(ρ−1) /2) −fraco e tem norma suficientemente pequena. / In this work, we discuss the well−posedness of the initial value problem for the semilinear heat equation. We show the existence of global mild solution, when the initial data u_0 belong to weak L^(n(ρ−1)/ 2) space with a sufficiently small norm.

Este trabalho que envolve matemática aplicada e processamento paralelo: seu objetivo é avaliar uma estratégia de implementação em paralelo para algoritmos de diferenças finitas que aproximam a solução de equações diferenciais de evolução. A alternativa proposta é a substituição dos produtos matriz-vetor efetuados sequencialmente por multiplicações matriz-matriz aceleradas pelo método de Strassen em paralelo. O trabalho desenvolve testes visando verificar o ganho computacional relacionado a essa estratégia de paralelização, pois as aplicacações computacionais, que empregam a estratégia sequencial, possuem como característica o longo período de computação causado pelo grande volume de cálculo. Inclusive como alternativa, nós usamos o algoritmo em paralelo convencional para solução de algoritmos explícitos para solução de equações diferenciais parciais evolutivas no tempo. Portanto, de acordo com os resultados obtidos, nós observamos as características de cada estratégia em paralelo, tendo como principal objetivo diminuir o esforço computacional despendido. / This work involves parallel processing and applied mathematics: Our goal is to evaluate a strategy for implementing parallel algorithms for finite diference approach,it is the solution of diferential equations of evolution. The alternative proposed is the replacement of the matrix-vector products performed sequentially by matrix-matrix multiplication method accelerated by Strassen in parallel. The work develops tests in order to verify the speedup related to the strategy of parallelization because sequential application have characterized for long periods of computation, this is caused by the large amount of calculation. Even alternatively, we use the algorithm in parallel to conventional explicit solution algorithms for solving partial diferential equations. Therefore, according to the results, we observe the characteristics of each strategy in parallel with the main purpose of reducing the computational effort expended.

Made available in DSpace on 2015-05-15T11:46:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 425597 bytes, checksum: 2cb5c42e376ba77764139fbc3fcdaf15 (MD5) Previous issue date: 2011-07-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / We consider the semilinear heat equation involving gradient terms in a bounded domain of Rn. It is assumed the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when the control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the control may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints. / Consideremos a equação do calor semilinear envolvendo termos do gradiente em um domínio limitado do Rn. Assumimos que a não-linearidade é globalmente Lipschtz. Usando o método do ponto fixo, provamos que o sistema é finito-aproximadamente controlável e nulamente controlável, quando o controle age em um subconjunto não vazio do domínio.