This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.
Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear an...n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.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
We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×...We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×(0,T], u（±1,t）=0,u（x,0）=■（x）, where a is strongly nonlinear with respect to u<sub>xx</sub>and ■ is not necessarily small.We also deal with nonuniform case.展开更多
In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation u_t-div(|?u|^(p-2)?u) =-|u|^(β-1) u + α|u|^(q-2 )u,where p > 1, β > 0, q≥1 and α > 0. By using Gagliard...In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation u_t-div(|?u|^(p-2)?u) =-|u|^(β-1) u + α|u|^(q-2 )u,where p > 1, β > 0, q≥1 and α > 0. By using Gagliardo-Nirenberg type inequality, the energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents.展开更多
The calculation equation of large diameter bored pile＇s effective length is connected with its distribution of pile shaft resistance. Thus, there is a great difference between the calculation results under the differ...The calculation equation of large diameter bored pile＇s effective length is connected with its distribution of pile shaft resistance. Thus, there is a great difference between the calculation results under the different distributions of pile shaft resistance. Primarily, this paper summarizes the conceptualized mode of pile shaft resistance under the circum- stance that the soil surrounding the piles presents different layer distributions. Secondly, based on Mindlin＇s displacement solution and in consideration of the effect of pile diam- eter, the calculation equation is optimized with the assumption that the pile shaft resis- tance has a parabolic distribution. The influencing factors are analyzed according to the calculation result of effective pile length. Finally, combined with an engineering example, the calculation equation deduced in this paper is analyzed and verified. The result shows that both the Poisson ratio of soil and pile diameter have impacted the effective pile length. Compared with the Poisson ratio of soil, the effect of pile diameter is more significant. If the pile diameter remains the same, the effect of the Poisson ratio of soil to the effective pile length decreases as the ratio of pile elastic modulus and soil share modulus increases. If the Poisson ratio of soil remains the same, the effect of the pile diameter to the effective pile length increases as the ratio of pile elastic modulus and soil share modulus increases. Thus the optimized calculation result of pile effective length under the consideration of pile diameter effect is more close to the actual situation of engineering and reasonably practicable.展开更多
文摘This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.
文摘Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
文摘n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.
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 Open Office of Mathematica Institute,Academia Sinica.
文摘We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×(0,T], u（±1,t）=0,u（x,0）=■（x）, where a is strongly nonlinear with respect to u<sub>xx</sub>and ■ is not necessarily small.We also deal with nonuniform case.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371286 and 11401458)the Special Fund of Education Department (Grant No. 2013JK0586)the Youth Natural Science Grant of Shaanxi Province of China (Grant No. 2013JQ1015)
文摘In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation u_t-div(|?u|^(p-2)?u) =-|u|^(β-1) u + α|u|^(q-2 )u,where p > 1, β > 0, q≥1 and α > 0. By using Gagliardo-Nirenberg type inequality, the energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents.
基金supported by the National Natural Science Foundation of China(51208047)
文摘The calculation equation of large diameter bored pile＇s effective length is connected with its distribution of pile shaft resistance. Thus, there is a great difference between the calculation results under the different distributions of pile shaft resistance. Primarily, this paper summarizes the conceptualized mode of pile shaft resistance under the circum- stance that the soil surrounding the piles presents different layer distributions. Secondly, based on Mindlin＇s displacement solution and in consideration of the effect of pile diam- eter, the calculation equation is optimized with the assumption that the pile shaft resis- tance has a parabolic distribution. The influencing factors are analyzed according to the calculation result of effective pile length. Finally, combined with an engineering example, the calculation equation deduced in this paper is analyzed and verified. The result shows that both the Poisson ratio of soil and pile diameter have impacted the effective pile length. Compared with the Poisson ratio of soil, the effect of pile diameter is more significant. If the pile diameter remains the same, the effect of the Poisson ratio of soil to the effective pile length decreases as the ratio of pile elastic modulus and soil share modulus increases. If the Poisson ratio of soil remains the same, the effect of the pile diameter to the effective pile length increases as the ratio of pile elastic modulus and soil share modulus increases. Thus the optimized calculation result of pile effective length under the consideration of pile diameter effect is more close to the actual situation of engineering and reasonably practicable.
