In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear ...In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method(HPM) is also used to solve these equations; finally,approximate solutions by HAM of(2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3 rd-order approximation solutions by HAM and HPM have great fluctuation.展开更多
By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero soluti...In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.展开更多
文摘In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method(HPM) is also used to solve these equations; finally,approximate solutions by HAM of(2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3 rd-order approximation solutions by HAM and HPM have great fluctuation.
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
文摘In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.
