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APPROXIMATION OF SOLUTION OF LINEAR DIFFERENTIAL EQUATION WITH ALMOST PERIOD FUNCTION COEFFICIENTS
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作者 蔡海涛 黄伯云 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期503-508,共6页
This paper is devoted to the study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of gen... This paper is devoted to the study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear differential equation for infinite interval case. For finite interval case, this equation was investigated by G. Tamarkin([1]) applying the Picard method of successive approximation. 展开更多
关键词 approximation almost period function Picard method of successive approximation
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ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION 被引量:5
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作者 徐艳玲 蒋咪娜 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期119-129,共11页
This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove t... This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut + f(u)x = 0 with Riemann initial data u(x, 0) = 展开更多
关键词 Burgers equation rarefaction wave the method of successive approximation maximum principle a priori estimatc STABILITY
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Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm
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作者 Alexey Shcheglov Jingzhi Li +2 位作者 Chao Wang Alexander Ilin Ye Zhang 《Advances in Applied Mathematics and Mechanics》 SCIE 2024年第1期237-252,共16页
This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse probl... This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach. 展开更多
关键词 Inverse problem quasi-linear dynamic model UNIQUENESS method of successive approximations stability
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