$\left\{{l@{\quad}l}u_t(x, t) = J*u(x, t)-u(x, t) + u^p(x, t), & \qquad x \in \mathbb{R}^N,\; t > 0,\\ u(x, 0) = u_0(x), & \qquad x \in\mathbb{R}^N,\right.$\left\{\begin{array}{l@{\quad}l}u_t(x, t) = J*u(x, t)-u(x, t) + u^p(x, t), & \qquad x \in \mathbb{R}^N,\; t > 0,\\ u(x, 0) = u_0(x), & \qquad x \in\mathbb{R}^N,\end{array}\right. 相似文献
11.
12.
C. R. Ortloff 《Journal of Optimization Theory and Applications》1968,2(1):65-80
Rosen's restricted variational principle representation of the Boltzmann equation is applied to the problem of determining the transitional-regime, low-density, hypersonic flow over slender, conical vehicles with diffusely reflecting surfaces. If the trial distribution function is suitably chosen, the Euler-Lagrange equations associated with Rosen's functional result in a semilinear hyperbolic system amenable to solution by classical characteristics methods. Sample calculations are given and compared with the low-density cone flow experiments of Hickman to assess the accuracy of the method presented. It is believed that the present method constitutes the first solution method for boundary value problems in the low-density transitional flow regime.This work was supported by the United States Air Force, Contract No. AF04(695)-1001. 相似文献
13.
Euler-Lagrange and Euler-Hamilton variational principles are presented for a class of linear initial value problems. 相似文献
14.
The validity of the variational principle for scattering problems is examined in the case of ionization of atomic hydrogen by electron impact. The effective charge seen by the scattered electron is determined mathematically in a rigorous way excluding any empirical assumptions. It is shown that the elaborated approach gives effective charge values that are reasonable and have clear physical meaning. 相似文献
15.
A new definition of the dimension of probability measures is introduced. It is related with the fractal dimension of sets by a variational principle. This principle is applied in the theory of iterated function systems. 相似文献
16.
We verify – after appropriate modifications – an old conjecture of Brezis-Ekeland ([3], [4]) concerning the feasibility of a global variational approach to the problems of existence and uniqueness of gradient flows for convex energy functionals. Our approach is based on a concept of self-duality inherent in many parabolic evolution equations, and motivated by Bolza-type problems in the classical calculus of variations. The modified principle allows to identify the extremal value –which was the missing ingredient in [3]– and so it can now be used to give variational proofs for the existence and uniqueness of solutions for the heat equation (of course) but also for quasi-linear parabolic equations, porous media, fast diffusion and more general dissipative evolution equations.Both authors were partially supported by a grant from the Natural Science and Engineering Research Council of Canada.This paper is part of this authors Masters thesis under the supervision of the first named author.Revised version: 31 March 2004 相似文献
17.
A variational principle for domino tilings 总被引:8,自引:0,他引:8
Henry Cohn Richard Kenyon James Propp 《Journal of the American Mathematical Society》2001,14(2):297-346
We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can be described by a function that maximizes an entropy integral. We associate an entropy to every sort of local behavior domino tilings can exhibit, and prove that almost all tilings lie within (for an appropriate metric) of the unique entropy-maximizing solution. This gives a solution to the dimer problem with fully general boundary conditions, thereby resolving an issue first raised by Kasteleyn. Our methods also apply to dimer models on other grids and their associated tiling models, such as tilings of the plane by three orientations of unit lozenges. 18.
M. V. Uvarova 《Siberian Advances in Mathematics》2011,21(3):211-231
In the Sobolev-Besov spaces, we examine the question on solvability of nonlocal boundary value problems for operator-differential
equations of the form
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