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Academic literature on the topic 'Conjugate boundary value problems'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Conjugate boundary value problems"

1

Agarwal, R. P., and D. O'Regan. "Discrete conjugate boundary value problems." Applied Mathematics Letters 13, no. 2 (February 2000): 97–104. http://dx.doi.org/10.1016/s0893-9659(99)00171-8.

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Li, Weifeng, and Jinyuan Du. "Linear conjugate boundary value problems." Wuhan University Journal of Natural Sciences 12, no. 6 (November 2007): 985–91. http://dx.doi.org/10.1007/s11859-007-0037-5.

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Chuan-Rong, Wang, and Yang Qiao-Lin. "Linear conjugate boundary value problems." Complex Variables, Theory and Application: An International Journal 31, no. 2 (October 1996): 105–19. http://dx.doi.org/10.1080/17476939608814952.

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Palamides, P. K. "Conjugate boundary value problems, via Sperner's lemma." Nonlinear Analysis: Theory, Methods & Applications 46, no. 2 (October 2001): 299–308. http://dx.doi.org/10.1016/s0362-546x(00)00124-3.

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Wong, P. J. Y. "Triple positive solutions of conjugate boundary value problems." Computers & Mathematics with Applications 36, no. 9 (November 1998): 19–35. http://dx.doi.org/10.1016/s0898-1221(98)00190-4.

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Agarwal, Ravi P., Martin Bohner, and Patricia J. Y. Wong. "Positive solutions and eigenvalues of conjugate boundary value problems." Proceedings of the Edinburgh Mathematical Society 42, no. 2 (June 1999): 349–74. http://dx.doi.org/10.1017/s0013091500020307.

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We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.

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Yao, Qingliu. "Positive solution to a singular $(k,n-k)$ conjugate boundary value problem." Mathematica Bohemica 136, no. 1 (2011): 69–79. http://dx.doi.org/10.21136/mb.2011.141451.

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Wong, Patricia J. Y., and Ravi P. Agarwal. "Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems." gmj 6, no. 6 (December 1999): 567–90. http://dx.doi.org/10.1515/gmj.1999.567.

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Abstract We consider the boundary value problem 𝑦(𝑛) (𝑡) = 𝑃(𝑡, 𝑦), 𝑡 ∈ (0, 1) 𝑦(𝑗) (𝑡𝑖) = 0, 𝑗 = 0, . . . , 𝑛𝑖 – 1, 𝑖 = 1, . . . , 𝑟, where 𝑟 ≥ 2, 𝑛𝑖 ≥ 1 for 𝑖 = 1, . . . , 𝑟, and 0 = 𝑡1 < 𝑡2 < ⋯ < 𝑡𝑟 = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.

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Davis, John M., Paul W. Eloe, and Johnny Henderson. "Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems." gmj 6, no. 5 (October 1999): 415–20. http://dx.doi.org/10.1515/gmj.1999.415.

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Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.

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Kaufmann, Eric R., and Nickolai Kosmatov†. "Singular Conjugate Boundary Value Problems on a Time Scale." Journal of Difference Equations and Applications 10, no. 2 (February 2004): 119–27. http://dx.doi.org/10.1080/1023619031000114332.

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Dissertations / Theses on the topic "Conjugate boundary value problems"

1

Degla, Guy Aymard. "A Maximum Principle for Conjugate BVPs." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/4320.

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Hopkins, Britney Henderson Johnny. "Multiplicity of positive solutions of even-order nonhomogeneous boundary value problems." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5323.

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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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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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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 associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.

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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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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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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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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 solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.

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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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Books on the topic "Conjugate boundary value problems"

1

Boundary value problems. Singapore: World Scientific, 2000.

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2

Powers, David L. Boundary value problems. 3rd ed. San Diego: Harcourt Brace Jovanovich, 1987.

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3

Mackie, A. G. Boundary value problems. Edinburgh: Scottish Academic Press, 1989.

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Boundary value problems. 4th ed. San Diego, CA: Academic Press, 1999.

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5

Gakhov, F. D. Boundary value problems. New York: Dover, 1990.

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6

Eidelman, Samuil D., and Nicolae V. Zhitarashu. Parabolic Boundary Value Problems. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8767-0.

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Hoffmann, K. H., and J. Sprekels, eds. Free Boundary Value Problems. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7301-7.

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Gazzola, Filippo, Hans-Christoph Grunau, and Guido Sweers. Polyharmonic Boundary Value Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12245-3.

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V, Zhitarashu N., ed. Parabolic boundary value problems. Basel: Birkhäuser Verlag, 1998.

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10

Bick, T. A. Elementary boundary value problems. New York: M. Dekker, 1993.

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Book chapters on the topic "Conjugate boundary value problems"

1

Agarwal, Ravi P., Donal O’Regan, and Patricia J. Y. Wong. "Conjugate Boundary Value Problems." In Positive Solutions of Differential, Difference and Integral Equations, 236–60. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9171-3_16.

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Agarwal, Ravi P., Donal O’Regan, and Patricia J. Y. Wong. "Discrete Conjugate Boundary Value Problems." In Positive Solutions of Differential, Difference and Integral Equations, 353–69. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9171-3_21.

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Litvinchuk, Georgii S. "Solvability theory of singular integral equations with a Carleman shift and complex conjugated boundary values in the degenerated and stable cases." In Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift, 177–205. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4363-9_5.

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Rajabov, Nusrat. "Linear Conjugate Boundary Value Problems for First Order Ordinary System of Linear Differential Equations with Singular or Super Singular Coefficients." In Proceedings of the Second ISAAC Congress, 175–83. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0269-8_23.

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Kress, Rainer. "Boundary Value Problems." In Graduate Texts in Mathematics, 257–86. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0599-9_11.

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Struchtrup, Henning. "Boundary value problems." In Macroscopic Transport Equations for Rarefied Gas Flows, 197–228. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-32386-4_12.

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Betounes, David. "Boundary Value Problems." In Partial Differential Equations for Computational Science, 145–84. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-2198-2_7.

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Khoury, Richard, and Douglas Wilhelm Harder. "Boundary Value Problems." In Numerical Methods and Modelling for Engineering, 285–306. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21176-3_13.

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Ahmad, Shair, and Antonio Ambrosetti. "Boundary value problems." In UNITEXT, 275–92. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16408-3_13.

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Soetaert, Karline, Jeff Cash, and Francesca Mazzia. "Boundary Value Problems." In Solving Differential Equations in R, 187–205. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28070-2_10.

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Conference papers on the topic "Conjugate boundary value problems"

1

Wang, Shuli, and Jianming Zhang. "Positive Solutions of 𝓂-point Conjugate Boundary Value Problems." In 2007 8th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing. IEEE, 2007. http://dx.doi.org/10.1109/snpd.2007.459.

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Webb, J. R. L., Alberto Cabada, Eduardo Liz, and Juan J. Nieto. "Higher order non-local (n−1,1) conjugate type boundary value problems." In MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE: International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine. AIP, 2009. http://dx.doi.org/10.1063/1.3142949.

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DeLillo, Thomas K., Tomasz Hrycak, and Nicolas Valdivia. "Iterative Regularization Methods for Inverse Problems in Acoustics." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32730.

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We consider the use of conjugate-gradient-like iterative methods for the solution of integral equations arising from an inverse problem in acoustics in a bounded three dimensional region. The inverse problem is the computation of the normal velocities on the boundary of a region from pressure measurements on an interior surface. The pressure satisfies the Helmholtz equation in the region. Two formulations are considered: one based on the representation of pressures by a single layer potential and the other based on the Helmholtz-Kirchhoff integral equation. Both formulations can be used to approximate the Neumann Green’s function as an alternative. The integral equations are all ill-posed and are discretized by a boundary element method. The resulting liner systems are ill-conditoned and a (smooth) regularized solutions must be sought. Two regularization rules, including a new one, for conjugate-gradient-like methods are applied and found to have advantages over a standard method based on the truncated singular value decomposition using generalized cross validation. Due to the occurence of multiple singular values for our integral operators, conjugate gradient methods compute the optimal solution in the first few iterations and prove to be particularly fast for these large scale acoustics problems.

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Grigoriev, M. M., and G. F. Dargush. "A Fast Multi-Level Boundary Element Method for the Steady Heat Diffusion Equation." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47450.

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A fast, accurate and efficient multi-level boundary element method is developed to solve general boundary value problems. Here we concentrate on problems of two-dimensional steady potential flow and present a fast direct boundary element formulation. This novel method extends the pioneering work of Brandt and Lubrecht on multi-level multi-integration (MLMI) in several important ways to address problems with mixed boundary conditions. We utilize bi-conjugate gradient methods (BCGM) and implement the MLMI approach for fast matrix and matrix transpose multiplication for every iteration loop. Furthermore, by introducing a C-cycle multigrid algorithm, we find that the number of iterations for the bi-conjugate gradient methods is independent of the boundary element mesh discretization for problems of steady-state heat diffusion considered in this paper. As a result, the computational complexity of the proposed method is proportional to only N · log(N), where N is the number of degrees of freedom.

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Siddique, Waseem, Torsten H. Fransson, and Lamyaa A. El-Gabry. "Improved Design of Internally Cooled Trailing Edge at Engine Similar Conditions: A Conjugate Heat Transfer Problem." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68557.

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Gas turbines are operated at elevated temperatures as the thermal efficiency of the gas turbine is directly linked to the turbine inlet gas temperature. The different regions of the turbine blade require different means of cooling. This paper presents different designs of the two-pass trapezoidal channel which represents the trailing edge of a real engine. Engine similar boundary conditions are applied and conjugate heat transfer method is used to predict the wall temperatures. The aim is to design a cooling channel that through use of steam can reduce wall temperatures to below a target value while maintaining minimal pressure drop. The variations in design of a smooth two-pass channel were made to achieve the design target. These variations included installation of ribs at the walls, tapered divider wall, tilted divider wall and L-shaped divider wall to promote fluid impingement on the trailing wall. The results suggest that a channel with staggered ribs at the outlet pass, a tilted divider wall and impingement at the corner is the best arrangement for reducing wall temperatures below the target value; however, it has low overall aerothermal performance due to high pressure losses. A similar channel without impingement can yield acceptable results if a thermal barrier coating is applied or if a small corner of the tip-trailing edge is truncated to reduce material volume. This modification though can improve the thermal performance of the channel, is to result in higher profile and aerodynamics losses.

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Wang, Zhenfeng, Peigang Yan, Hongyan Huang, and Wanjin Han. "Coupled BEM and FDM Conjugate Analysis of a Three-Dimensional Air-Cooled Turbine Vane." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-59030.

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A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a three-dimensional air-cooled turbine blade. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. In the fluid region, computation code (HIT-NS CODE) adopts the FDM to solve the Navier-Stokes equations. In the solid region, the BEM is adopted to resolve the conduction heat transfer equations. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The solid heat transfer computation code (3D-BEM CODE) is validated by comparing with the results of an analytic solution and the results of commercial code, the results from 3D-BEM CODE have a good agreement with the analytic solution and commercial code results. The BEM uses a weighted residual method to make the Laplace equation convert into a surface integral equation and the surface integral equation is discretized. The BEM avoids the complicated mesh needed in other computation methods and saves the computation time. In addition, the BEM has the characteristic of a combination of an analytic and a discrete solution. So the BEM solutions of heat conduction problems are more accurate. The results of the coupling computation code (HIT-NS-3DBEM CODE) have a good agreement with the experimental results. The adiabatic condition result is different from the results of experiment and code calculation. So the results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines. Four turbulence models are applied: K-epsilon model, K-omega model, K-omega (SST-Gamma Theta) model, and B-L model adopted by computation code. Different turbulence models gives different the results of vane wall temperature. Comparing the four turbulence models, the different turbulence models can exactly simulate the flow field, but they can not give exact values for the heat conduction simulation in the boundary layer. The result of K-Omega (SST-Gamma Theta) turbulence model is closer to the experimental data.

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Wang, Zhenfeng, Peigang Yan, Hongfei Tang, Hongyan Huang, and Wanjin Han. "The Simulation Study of Turbulence Models for Conjugate Heat Transfer Analysis of a High Pressure Air-Cooled Gas Turbine." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22088.

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The different turbulence models are adopted to simulate NASA-MarkII high pressure air-cooled gas turbine. The experimental work condition is Run 5411. The paper researches that the effect of different turbulence models for the flow and heat transfer characteristics of turbine. The turbulence models include: the laminar turbulence model, high Reynolds number k-ε turbulence model, low Reynolds number turbulence model (k-ω standard format, k-ω-SST and k-ω-SST-γ-θ) and B-L algebra turbulence model which is adopted by the compiled code. The results show that the different turbulence models can give good flow characteristics results of turbine, but the heat transfer characteristics results are different. Comparing to the experimental results, k-ω-SST-θ-γ turbulence model results are more accurate and can simulate accurately the flow and heat transfer characteristics of turbine with transition flow characteristics. But k-ω-SST-γ-θ turbulence model overestimates the turbulence kinetic energy of blade local region and makes the heat transfer coefficient higher. It causes that local region temperature is higher. The results of B-L algebra turbulence model show that the results of B-L model are accurate besides it has 4% temperature error in the transition region. As to the other turbulence models, the results show that all turbulence models can simulate the temperature distribution on the blade pressure surface except the laminar turbulence model underestimates the heat transfer coefficient of turbulence flow region. On the blade suction surface with transition flow characteristics, high Reynolds number k-ε turbulence model overestimates the heat transfer coefficient and causes the blade surface temperature is high about 90K than the experimental result. Low Reynolds number k-ω standard format and k-ω-SST turbulence models also overestimate the blade surface temperature value. So it can draw a conclusion that the unreasonable choice of turbulence models can cause biggish errors for conjugate heat transfer problem of turbine. The combination of k-ω-SST-γ-θ model and B-L algebra model can get more accurate turbine thermal environment results. In addition, in order to obtain the affect of different turbulence models for gas turbine conjugate heat transfer problem. The different turbulence models are adopted to simulate the different computation mesh domains (First case and Second case). As to each cooling passages, the first case gives the wall heat transfer coefficient of each cooling passages and the second case considers the conjugate heat transfer course between the cooling passages and blade. It can draw a conclusion that the application of heat transfer coefficient on the wall of each cooling passages avoids the accumulative error. So, for the turbine vane geometry models with complex cooling passages or holes, the choice of turbulence models and the analysis of different mesh domains are important. At last, different turbulence characteristic boundary conditions of turbine inner-cooling passages are given and K-ω-SST-γ-θ turbulence model is adopted in order to obtain the effect of turbulence characteristic boundary conditions for the conjugate heat transfer computation results. The results show that the turbulence characteristic boundary conditions of turbine inner-cooling passages have a great effect on the conjugate heat transfer results of high pressure gas turbine.

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Ruan, Yougang, and Zhenping Feng. "Adjoint Based Heat Conduction Optimization of Struts Parameters Within Hollow Blade." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59422.

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Abstract In gas turbine, the interaction between hot gas mainstream and blade solid region becomes more and more obvious as the turbine inlet temperature increases, thus heat conduction within the blade solid regions should be taken into consideration in optimization design process. In this paper, an adjoint-based optimization method for heat conduction problems in the solid region was built based on ANSYS Fluent and OpenFOAM Solver. The continuous adjoint equation and the corresponding boundary conditions for three typical conduction boundary conditions were derived in detail. To validate the correctness of this method, inverse design problems within the hollow cylinder and hollow blade were calculated, respectively. Inner shape inverse design of the hollow cylinder and the blade thickness inverse design were performed, and the target values were found successfully. Adjoint gradients were compared with finite-difference method or theoretical results. Then a Conjugate Heat Transfer (CHT) calculation was performed using ANSYS Fluent software, and the numerical methods were validated against the experimental results. An optimization of the struts place and thickness within hollow blade for average temperature was performed based on the CHT calculation results. Average temperature within the solid region of the optimized blade decreased 11.1K as compared to the original case.

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Nistri, Paolo. "Nonlinear boundary value control problems." In 1986 25th IEEE Conference on Decision and Control. IEEE, 1986. http://dx.doi.org/10.1109/cdc.1986.267376.

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Vasilyev, Vladimir. "On discrete boundary value problems." In INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000647.

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Reports on the topic "Conjugate boundary value problems"

1

Greengard, L. Spectral Integration and Two-Point Boundary Value Problems. Fort Belvoir, VA: Defense Technical Information Center, August 1988. http://dx.doi.org/10.21236/ada199805.

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Wiener, Joseph. Boundary Value Problems for Differential and Functional Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada187378.

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Greengard, L., and V. Rokhlin. On the Numerical Solution of Two-Point Boundary Value Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1989. http://dx.doi.org/10.21236/ada211244.

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Garbey, M., and H. G. Kaper. Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems. Office of Scientific and Technical Information (OSTI), April 1995. http://dx.doi.org/10.2172/510563.

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Keller, H. B., and H. O. Kreiss. Mathematical Software for Hyperbolic Equations and Two Point Boundary Value Problems. Fort Belvoir, VA: Defense Technical Information Center, February 1985. http://dx.doi.org/10.21236/ada151982.

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Pieper, G. Proceedings of the focused research program on spectral theory and boundary value problems. Office of Scientific and Technical Information (OSTI), August 1989. http://dx.doi.org/10.2172/5634269.

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Pieper, G. W. Proceedings of the focused research program on spectral theory and boundary value problems: Volume 3, Linear differential equations and systems. Office of Scientific and Technical Information (OSTI), April 1989. http://dx.doi.org/10.2172/6023178.

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R. Axford. Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems. Office of Scientific and Technical Information (OSTI), August 2002. http://dx.doi.org/10.2172/810261.

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Just, Richard E., Eithan Hochman, and Sinaia Netanyahu. Problems and Prospects in the Political Economy of Trans-Boundary Water Issues. United States Department of Agriculture, February 2000. http://dx.doi.org/10.32747/2000.7573997.bard.

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Abstract:

The objective of this research was to develop and apply a conceptual framework for evaluating the potential of trans-boundary bargaining with respect to water resource sharing. The research accomplished this objective by developing a framework for trans-boundary bargaining, identifying opportunities for application, and illustrating the potential benefits that can be gained thereby. Specifically, we have accomplished the following: - Developed a framework to measure the potential for improving economic efficiency considering issues of political feasibility and sustainability that are crucial in trans-boundary cooperation. - Used both cooperative and non-cooperative game theory to assess feasible coalitions among the parties involved and to model potential bargaining procedures. - Identified empirically alternative schemes of cooperation that both improve upon the economic efficiency of present water usage and appease all of the cooperating parties. - Estimated the potential short-run and long-run affects of water reallocation on the agricultural sector and used this information to understand potential strategies taken by the countries in bargaining processes. - Performed case studies in Israeli-Jordanian relations, the relationship of Israel to the Palestinian Authority, and cooperation on the Chesapeake Bay. - Published or have in process publication of a series of refereed journal articles. - Published a book which first develops the theoretical framework, then presents research results relating to the case studies, and finally draws implications for water cooperation issues generally. Background to the Topic The increase in water scarcity and decline in water quality that has resulted from increased agricultural, industrial, and urban demands raises questions regarding profitability of the agricultural sector under its present structure. The lack of efficient management has been underscored recently by consecutive years of drought in Israel and increased needs to clean up the Chesapeake Bay. Since agriculture in the Middle East (Chesapeake Bay) is both the main water user (polluter) and the low-value user (polluter), a reallocation of water use (pollution rights) away from agriculture is likely with further industrial and urban growth. Furthermore, the trans-boundary nature of water resources in the case of the Middle East and the Chesapeake Bay contributes to increased conflicts over the use of the resources and therefore requires a political economic approach. Major Conclusions, Solutions, Achievements and Implications Using game theory tools, we critically identify obstacles to cooperation. We identify potential gains from coordination on trans-boundary water policies and projects. We identify the conditions under which partial (versus grand) coalitions dominate in solving water quality disputes among riparian countries. We identify conditions under which linking water issues to unrelated disputes achieves gains in trans-boundary negotiations. We show that gains are likely only when unrelated issues satisfy certain characteristics. We find conditions for efficient water markets under price-determined and quantity-determined markets. We find water recycling and adoption of new technologies such as desalination can be part of the solution for alleviating water shortages locally and regionally but that timing is likely to be different than anticipated. These results have been disseminated through a wide variety of publications and oral presentations as well as through interaction with policymakers in both countries.

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