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The well-known Derrida–Lebowitz–Speer–Spohn equation is investigated. By using specific ansätze and the classical symmetries of the equation, several families of new exact solutions have been found. In particular, there appear traveling waves that include compactons and soliton–compactons. Some other solutions conserve the mass and exhibit diffusion and convection processes from an instantaneous source and localized peakons.  相似文献   

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ABSTRACT

A nonlocal reaction–diffusion equation arising in various applications is studied. The speed of traveling waves is determined by means of a minimax representation. It is used to obtain the wave speed estimates and asymptotic values.  相似文献   

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Carlo de Falco  Joseph W. Jerome  Riccardo Sacco 《PAMM》2007,7(1):1130603-1130604
This communication describes a functional iteration technique, denoted Generalized Gummel Map (GGM), for the solution of the Quantum Drift–Diffusion (QDD) model. The assumptions needed to establish existence of a fixed point for the GGM are described and their plausibility is assessed via physical arguments supported by one–dimensional numerical experiments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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We study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift–diffusion model of a semiconductor. We prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions. We prove analytical estimates of the remainder terms of this asymptotic expansion, and confirm by means of numerical simulations that these remainder estimates are sharp.  相似文献   

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We give an example of a stochastic Hamilton–Jacobi equation du=H(Du)dξ which has an infinite speed of propagation as soon as the driving signal ξ is not of bounded variation.  相似文献   

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We study the stationary problem of the drift–diffusion model with a mixed boundary condition. For this problem, the existence of solutions was established in general settings, while the uniqueness was investigated only in some special cases which do not entirely cover situations that semiconductor devices are used in integrated circuits. In this paper, we prove the uniqueness in a physically relevant situation. The key to the proof is to derive two-sided uniform estimates for the densities of the electron and hole. We establish a new technique to show the lower bound. This together with the Moser iteration method leads to the upper bound.  相似文献   

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We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.  相似文献   

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We discuss asymptotic properties of solutions of two-component parabolic drift–diffusion systems coupled through an elliptic equation in two space dimensions. In particular, conditions for finite time blowup versus the existence of forward self-similar solutions are studied.  相似文献   

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The quasi-neutral limit in a bipolar drift–diffusion model for semiconductors with physical contact-insulating boundary conditions, the general sign-changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one-dimensional case. The dynamic structure stability of the solution with respect to the scaled Debye length is proven by the asymptotic analysis of singular perturbation and the entropy-energy method. The key point of the proof is to use sufficiently the fact that the ‘length’ of the boundary layer is very small in a short time period.  相似文献   

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We investigate several existing interface procedures for finite difference methods applied to advection–diffusion problems. The accuracy, stiffness and reflecting properties of various interface procedures are investigated.The analysis and numerical experiments show that there are only minor differences between various methods once a proper parameter choice has been made.  相似文献   

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We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians and how these elements satisfy the rational level-one quantum Knizhnik–Zamolodchikov equation in some cases.  相似文献   

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Bounds for the size of the support of a compactly supported momentum density of the Camassa–Holm equation are derived. This is achieved by estimating the first Dirichlet eigenvalue of the support. This elaborates the result on the preservation of its compactness, and gives more information on the velocity by estimating the size of the region where it is not that well understood.  相似文献   

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The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction–diffusion–advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.  相似文献   

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Direct and inverse boundary value problems for models of stationary reaction–convection–diffusion are investigated. The direct problem consists in finding a solution of the corresponding boundary value problem for given data on the boundary of the domain of the independent variable. The peculiarity of the direct problem consists in the inhomogeneity and irregularity of mixed boundary data. Solvability and stability conditions are specified for the direct problem. The inverse boundary value problem consists in finding some traces of the solution of the corresponding boundary value problem for given standard and additional data on a certain part of the boundary of the domain of the independent variable. The peculiarity of the inverse problem consists in its ill-posedness. Regularizing methods and solution algorithms are developed for the inverse problem.  相似文献   

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