共查询到20条相似文献,搜索用时 15 毫秒
1.
Yuri Bakhtin 《Proceedings of the American Mathematical Society》2007,135(7):2257-2262
We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.
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We consider the initial–boundary value problem for the KdV–Burgers equation posed on a bounded interval . This problem features non-homogeneous boundary conditions applied at and and is known to have unique global smooth solution. 相似文献
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In this work, multiple-front solutions for the Burgers equation and the coupled Burgers equations are examined. The tanh–coth method and the Cole–Hopf transformation are used. The work highlights the power of the proposed schemes and the structures of the obtained multiple-front solutions. 相似文献
4.
Alexander Gladkov Kwang Ik Kim 《Journal of Mathematical Analysis and Applications》2008,338(1):264-273
In this paper, we consider a semilinear heat equation ut=Δu+c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition and nonnegative initial data where p>0 and l>0. We prove global existence theorem for max(p,l)?1. Some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given. 相似文献
5.
Alvaro H. Salas 《Applied mathematics and computation》2010,216(1):18-3836
In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method. 相似文献
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S. Guerrero O.Yu. Imanuvilov 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2007,24(6):897-906
In this paper we deal with the viscous Burgers equation. We study the exact controllability properties of this equation with general initial condition when the boundary control is acting at both endpoints of the interval. In a first result, we prove that the global exact null controllability does not hold for small time. In a second one, we prove that the exact controllability result does not hold even for large time. 相似文献
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In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models. 相似文献
8.
Yan Zheng 《数学学报(英文版)》2016,32(12):1509-1514
The current paper is devoted to stochastic Burgers equation with driving forcing given by white noise type in time and periodic in space. Motivated by the numerical results of Hairer and Voss, we prove that the Burgers equation is stochastic stable in the sense that statistically steady regimes of fluid flows of stochastic Burgers equation converge to that of determinstic Burgers equation as noise tends to zero. 相似文献
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Ch. Srinivasa Rao P. L. Sachdev Mythily Ramaswamy 《Nonlinear Analysis: Real World Applications》2003,4(5):723-741
The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming certain asymptotic conditions at plus infinity or minus infinity, we find a wide variety of solutions—(positive) single hump, monotonic (bounded or unbounded) or solutions with a finite zero. The existence or non-existence of positive bounded solutions with exponential decay to zero at infinity for specific parameter ranges is proved. The analysis relies mainly on the shooting argument. 相似文献
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《Stochastic Processes and their Applications》2020,130(10):5973-5998
We consider the stationary O’Connell–Yor model of semi-discrete directed polymers in a Brownian environment in the intermediate disorder regime and show convergence of the increments of the log-partition function to the energy solutions of the stochastic Burgers equation.The proof does not rely on the Cole–Hopf transform and avoids the use of spectral gap estimates for the discrete model. The key technical argument is a second-order Boltzmann–Gibbs principle. 相似文献
12.
We study the well‐posedness and dynamic behavior for the KdV‐Burgers equation with a force on R . We establish L p ?L q estimates of the evolution , as an application we obtain the local well‐posedness. Then the global well‐posedness follows from a uniform estimate for solutions as t goes to infinity. Next, we prove the asymptotical regularity of solutions in space and by the smoothing effect of . The regularity and the asymptotical compactness in L 2 yields the asymptotical compactness in by an interpolation arguement. Finally, we conclude the existence of an globalattractor. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(4):821-829
This paper is concerned with the local and global existence of mild solution for an impulsive fractional functional integro differential equations with nonlocal condition. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The results are obtained by using the fixed point technique and solution operator on a complex Banach space. 相似文献
16.
Mustafa Inc 《Numerical Methods for Partial Differential Equations》2010,26(5):1224-1235
In this article, we present the Homotopy Perturbation Method (Shortly HPM) for obtaining the numerical solutions of the Korteweg‐de Vries Burgers (KdVB) equation. The series solutions are developed and the reccurance relations are given explicity. The initial approximation can be freely chosen with possibly unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very simple and effective. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
17.
In this paper we introduce and analyze a stochastic particle method for the McKean-Vlasov and the Burgers equation; the construction and error analysis are based upon the theory of the propagation of chaos for interacting particle systems. Our objective is three-fold. First, we consider a McKean-Vlasov equation in with sufficiently smooth kernels, and the PDEs giving the distribution function and the density of the measure , the solution to the McKean-Vlasov equation. The simulation of the stochastic system with particles provides a discrete measure which approximates for each time (where is a discretization step of the time interval ). An integration (resp. smoothing) of this discrete measure provides approximations of the distribution function (resp. density) of . We show that the convergence rate is for the approximation in of the cumulative distribution function at time , and of order for the approximation in of the density at time ( is the underlying probability space, is a smoothing parameter). Our second objective is to show that our particle method can be modified to solve the Burgers equation with a nonmonotonic initial condition, without modifying the convergence rate . This part extends earlier work of ours, where we have limited ourselves to monotonic initial conditions. Finally, we present numerical experiments which confirm our theoretical estimates and illustrate the numerical efficiency of the method when the viscosity coefficient is very small.
18.
Ibrahim E. Inan 《Applied mathematics and computation》2010,217(4):1294-1299
In this paper, we implemented the exp-function method for the exact solutions of the fifth order KdV equation and modified Burgers equation. By using this scheme, we found some exact solutions of the above-mentioned equations. 相似文献
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In this paper, we investigate the initial value problem for the nonlinear pseudo-parabolic equation. Global existence and optimal decay estimate of solution are established, provided that the initial value is suitably small. Moreover, when n?2 and the nonlinear term f(u) disappears, we prove that the global solutions can be approximated by the linear solution as time tends to infinity. When n=1 and the nonlinear term f(u) disappears, we show that as time tends to infinity, the global solution approaches the nonlinear diffusion wave described by the self-similar solution of the viscous Burgers equation. 相似文献
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