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1.
L. E. Payne P. W. Schaefer J. C. Song 《Mathematical Methods in the Applied Sciences》2004,27(17):2045-2053
Energy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
2.
We examine differences between3H binding energies obtained by solving the Faddeev equations using standard partial-wave expansion procedures and results from solving the Schrödinger equation by means of the coupled-rearrangement-channel variational method. Variational bounds generated from Faddeev solutions for several contemporary, realistic potential models are presented as a function of the number of partial waves retained in the potential expansion. We demonstrate that the Faddeev wave function yields an optimal variational bound for the partial-wave truncated potential from which it is generated, but it does not yield optimal bounds for the full Hamiltonian or when the potential is partial-wave truncated at a different level. Finally, qualitative differences between3H solutions for static models such as the AV14 and RSC potentials and for momentum-dependent models such as the Nijmegen soft-core and Paris potentials are explored, and comparison is made with solutions for the RSC/TM two-body-force plus three-body-force model. 相似文献
3.
L. E. Payne G. A. Philippin V. Proytcheva 《Mathematical Methods in the Applied Sciences》2007,30(15):1885-1898
In this paper, we investigate the continuous dependence on the geometry and the initial time for solutions u( x , t) of a class of nonlinear parabolic initial‐boundary value problems. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
We consider the Maxwell-Cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time. We obtain L2 bounds for the temperature and heat flux by means of Lagrange identities. These bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations. 相似文献
5.
6.
L.E. Payne 《Journal of Mathematical Analysis and Applications》2003,284(1):283-293
We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities. 相似文献
7.
L.E. Payne 《Journal of Mathematical Analysis and Applications》2007,335(1):371-376
In this paper we consider two different initial-boundary value problems in temperature dependent viscous flow when the temperature equation has a nonlinear heat source term. When blow-up occurs we derive lower bounds for the blow-up time in each case. 相似文献
8.
This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived. 相似文献
9.
H. A. Levine R. Quintanilla L. E. Payne 《Mathematical Methods in the Applied Sciences》1989,11(1):71-77
We consider a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs. 相似文献
10.
Philip W. Payne 《International journal of quantum chemistry》1982,22(6):1085-1152
Techniques of diagrammatic spin algebra are employed to derive segment factorization formulas for spin-adapted matrix elements of one- and two-electron excitation operators. The spin-adapted basis is formed by the Yamanouchi–;Kotani geneological coupling method, and therefore constitutes an irreducible basis of the unitary group U(N), as prescribed by Gel'fand and Tsetlin. Several features distinguish this paper from similar work that has recently been published. First, intermediate steps in the derivation of each segment factor are fully documented. Comprehensive tables list the spin diagrams and phases that contribute to the possible segment factors. Second, a special effort has been made to distinguish between those parts of a segment factor that can be ascribed to a spin diagram and those parts which arise from the orbitals. The results of this paper should thus be useful for those who wish to extend diagrammatic spin algebra to evaluation of matrix elements for states built from nonorthogonal orbitals. Third, a novel graphical method has been introduced to keep track of phase changes that are induced by line up permutations of creation and annihilation operators. This technique may be useful for extension of our analysis to higher excitations. The necessary concepts of second quantization and diagrammatic spin algebra are developed in situ, so the present derivation should be accessible to those who have little prior knowledge of such methods. 相似文献