This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers（BBM-Burgers） equation to the corresponding degenerate boundary layer solutions in the half-s...This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers（BBM-Burgers） equation to the corresponding degenerate boundary layer solutions in the half-space.It is shown that the convergence rate is t-（α/4） as t →∞ provided that the initial perturbation lies in H α 1 for α 〈 α（q）：= 3 ＋（2/q）,where q is the degeneracy exponent of the flux function.Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1]展开更多
§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if...§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if展开更多
In this paper,we study the existence and regularity of travelling wave front solutions for some degenerate parabolic equations (u^m/m)t=u_(xx)+u^nf(u),where m,n>0 and f(u)～1-u.We show that the existence and regula...In this paper,we study the existence and regularity of travelling wave front solutions for some degenerate parabolic equations (u^m/m)t=u_(xx)+u^nf(u),where m,n>0 and f(u)～1-u.We show that the existence and regularity of travelling wave front solutions depend on the parameters m,n and the wave speed c.展开更多
Based on the Hirota’s method,the multiple-pole solutions of the focusing Schr?dinger equation are derived directly by introducing some new ingenious limit methods.We have carefully investigated these multi-pole solut...Based on the Hirota’s method,the multiple-pole solutions of the focusing Schr?dinger equation are derived directly by introducing some new ingenious limit methods.We have carefully investigated these multi-pole solutions from three perspectives:rigorous mathematical expressions,vivid images,and asymptotic behavior.Moreover,there are two kinds of interactions between multiple-pole solutions:when two multiple-pole solutions have different velocities,they will collide for a short time;when two multiple-pole solutions have very close velocities,a long time coupling will occur.The last important point is that this method of obtaining multiple-pole solutions can also be used to derive the degeneration of N-breather solutions.The method mentioned in this paper can be extended to the derivative Schr?dinger equation,Sine-Gorden equation,mKdV equation and so on.展开更多
基金supported by the "Fundamental Research Funds for the Central Universities"the National Natural Science Foundation of China (10871151)
文摘This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers（BBM-Burgers） equation to the corresponding degenerate boundary layer solutions in the half-space.It is shown that the convergence rate is t-（α/4） as t →∞ provided that the initial perturbation lies in H α 1 for α 〈 α（q）：= 3 ＋（2/q）,where q is the degeneracy exponent of the flux function.Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1]
文摘§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if
基金This project is supported by the Notional Natural Science Foundation of China
文摘In this paper,we study the existence and regularity of travelling wave front solutions for some degenerate parabolic equations (u^m/m)t=u_(xx)+u^nf(u),where m,n>0 and f(u)～1-u.We show that the existence and regularity of travelling wave front solutions depend on the parameters m,n and the wave speed c.
基金supported by the Natural Science Foundation of Guangdong Province of China(No.2021A1515012214)the Science and Technology Program of Guangzhou(No.2019050001)+1 种基金National Natural Science Foundation of China(Nos.12175111)K C Wong Magna Fund in Ningbo University。
文摘Based on the Hirota’s method,the multiple-pole solutions of the focusing Schr?dinger equation are derived directly by introducing some new ingenious limit methods.We have carefully investigated these multi-pole solutions from three perspectives:rigorous mathematical expressions,vivid images,and asymptotic behavior.Moreover,there are two kinds of interactions between multiple-pole solutions:when two multiple-pole solutions have different velocities,they will collide for a short time;when two multiple-pole solutions have very close velocities,a long time coupling will occur.The last important point is that this method of obtaining multiple-pole solutions can also be used to derive the degeneration of N-breather solutions.The method mentioned in this paper can be extended to the derivative Schr?dinger equation,Sine-Gorden equation,mKdV equation and so on.
