共查询到20条相似文献,搜索用时 11 毫秒
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通过Chapman-Enskog展开技术和多尺度分析,建立了一种新的D1Q4带修正项的四阶格子Boltzmann模型,一类非线性偏微分方程从连续的Boltzmann方程得到正确恢复.统一了KdV和Burgers等已知方程类型的格子BGK模型,还首次给出了组合KdV-Burgers,广义Burgers—Huxley等方程... 相似文献
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V. B. Dmitriev 《Russian Mathematics (Iz VUZ)》2012,56(4):1-8
In this paper we study a nonlocal problem for a first-order partial differential equation with an integral condition instead
of the standard boundary one. We prove that the problem under consideration is uniquely solvable. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(4):1541-1553
In this paper we solve an initial‐boundary value problem that involves a pde with a nonlocal term. The problem comes from a cell division model where the growth is assumed to be stochastic. The deterministic version of this problem yields a first‐order pde; the stochastic version yields a second‐order parabolic pde. There are no general methods for solving such problems even for the simplest cases owing to the nonlocal term. Although a solution method was devised for the simplest version of the first‐order case, the analysis does not readily extend to the second‐order case. We develop a method for solving the second‐order case and obtain the exact solution in a form that allows us to study the long time asymptotic behaviour of solutions and the impact of the dispersion term. We establish the existence of a large time attracting solution towards which solutions converge exponentially in time. The dispersion term does not appear in the exponential rate of convergence. 相似文献
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We develop a dynamic structural model for the wealth of individual mortgagors in a mortgage pool. We model the process of default and prepayment and, by taking a limit as the pool size goes to infinity, derive a stochastic partial differential equation (SPDE) which can be used to describe the evolution of the loss process from the pool. We prove existence and uniqueness of solutions to this SPDE and show how our model is able to capture, in a flexible way, the prices of credit risky tranches of mortgage-backed securities under different market conditions. 相似文献
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Weidong Lu. 《Mathematics of Computation》1998,67(222):593-602
A Cauchy problem for a one-dimensional diffusion-reaction equation is solved on a grid by a random walk method, in which the diffusion part is solved by random walk of particles, and the (nonlinear) reaction part is solved via Euler's polygonal arc method. Unlike in the literature, we do not assume monotonicity for the initial condition. It is proved that the algorithm converges and the rate of convergence is of order , where is the spatial mesh length.
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Yi‐Fei Pu Patrick Siarry Ji‐Liu Zhou Ni Zhang 《Mathematical Methods in the Applied Sciences》2014,37(12):1784-1806
Traditional integer‐order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method—fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer‐order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer‐order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high‐frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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H. Kunita 《Journal of Theoretical Probability》1994,7(2):279-308
We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)°
0,t
–1
, whereT(t) is a stochastic process with values in distributions and
s,t
is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC
-function under a condition similar to Hörmander's hypoellipticity condition. 相似文献
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In this paper, a fractional partial differential equation subject to the Robin boundary condition is considered. Based on the properties of Riemann-Liouville fractional derivative and a generalized Riccati technique, we obtained sufficient conditions for oscillation of the solutions of such equation. Examples are given to illustrate the main results. 相似文献
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Richard E. Ewing 《Journal of Mathematical Analysis and Applications》1979,71(1):167-186
Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. 相似文献
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A. V. Pskhu 《Differential Equations》2011,47(3):382-392
We construct a fundamental solution of a linear fractional partial differential equation. For an equation with Dzhrbashyan-Nersesyan
fractional differentiation operators, we solve a boundary value problem and find a closed-form representation for its solution.
The corresponding results for equations with Riemann-Liouville and Caputo derivatives are special cases of the assertions
proved here. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2486-2492
This paper deals with a partial differential equation by making use of the qualitative theory of differential equation. The main results are twofold. First, this work improves the previous result by analyzing the qualitative behavior of degenerate singular points. Second, new types of cusped solitons are obtained by setting the partial differential equation under inhomogeneous boundary condition. Asymptotic analysis and numerical simulations are provided for the cusped solitons of the equation. 相似文献
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The aim of this paper is to establish the existence of weak solutions to a steady state two-dimensional irrotational compressible flow around a thin profile. This flow is described by the small disturbance equations. If the speed of sound exceeds the fluid one, the governing equations remain elliptic. But when the fluid speed is beyond the sound one, the flow becomes locally hyperbolic and shock waves arise. For a modified elliptic model, using convexity arguments, we prove the existence of a solution which is the solution to the first model when the flow remains subsonic. 相似文献
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Nathaniel Chafee 《Journal of Differential Equations》1974,15(3):522-540
We consider a parabolic partial differential equation ut = uxx + f(u), where ? ∞ < x < + ∞ and 0 < t < + ∞. Under suitable hypotheses pertaining to f, we exhibit a class of initial data φ(x), ? ∞ < x < + ∞, for which the corresponding solutions u(x, t) approach zero as t → + ∞. This convergence is uniform with respect to x on any compact subinterval of the real axis. 相似文献
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Ruth F Curtain 《Journal of Mathematical Analysis and Applications》1981,79(2):352-369
Stochastic partial differential equations such as occur in vibration problems for mechanical structures subjected to random loading are modelled as infinite dimensional stochastic Itô differential equations using a semigroup approach. Sufficient conditions for exponential stability of the expected energy of the system, as well as for the exponential decay of the sample paths of the displacement and velocity, are given. Under these same conditions it is shown that the zero solution is pathwise asymptotically stable relative to finite dimensional initial conditions. Illustrative examples are included. 相似文献