带色散项的周期可积Hunter-Saxton方程的波的破裂

本文考虑一个带色散项的可积Hunter-Saxton方程的周期柯西问题.首先,我们得出该模型的强解的一个精确的爆破机制.其次,利用守恒量和特征方法,分别建立了有限时间内强解的爆破发生的充分条件.最后,给出了强解的爆破率.     

具非局部源反应扩散方程组解的同时爆破与不同时爆破

本文讨论具齐次Dirichlet边界条件非局部源反应扩散方程组的爆破解,给出四类同时爆破与不同时爆破现象的判定指标,这四类爆破现象包含:(i)存在不同时爆破;(ii)同时爆破与不同时爆破共存;(iii)任意爆破必是同时爆破;(iv)任意爆破必是不同时爆破.     

一般的两个分量的Dullin-Gottwald-Holm系统解的爆破与无限传播速度

考虑一般的两个分量的Dullin-Gottwald-Holm(GDGH2)系统解的爆破和无限传播速度.首先,给出了一个保证强解发生爆破的新的充分条件.然后,证明了对GDGH2的非平凡古典解而言,初始值u_0(x)和ρ_0(x)有紧支集不能保证相应的解有紧支集.     

一类反应扩散系统的不同时爆破临界指标(英文)

本文讨论了一类反应扩散方程组齐次第一初边值问题u_t=△u+u~mv~p,v_t=△v+u~qv~n的不同时爆破临界指标问题.在一定初值条件下,本文给出了径向解的四种同时、不同时爆破现象:存在初值使得同时爆破或不同时爆破发生;任何爆破均是同时或不同时的.通过对指标参数的完整分类给出了四种爆破现象的充分必要条件,并且得到了解的全部爆破速率估计.所得结果推广了以前的相应工作.     

一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

在齐次Dirichlet边界条件研究如下抛物系统其中x_0(t):R⁺→(0,a)是Holder连续函数;常数0≤α,β<1,p_1,p_2,q_1,q_2,k_1,k_2>0.利用正则化方法,在一定的假设条件下证明了经典解的存在性.接着利用比较原理证明了该系统正解的整体存在性和爆破性.最后给出了爆破解的精确爆破速率和爆破模式.     

具有趋化性的非线性系统的解的爆破性态分析

讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.     

具有Neumann边界条件热方程组的爆破速度

本文考虑具有 Ｎｅｕｍａｎｎ边界条件 ｕ／ｎ＝ｅｖ, ｖ／η＝ｅｕ在 ＳＲ ×（０,Ｔ）热方程组。ｕｔ＝△ｕ,ｖｔ=△ｖ在ＢＲ×（０,Ｔ）解的爆破性质·我们给出了爆破速度估计并证明了爆破仅在边界上发生．     

耗散Boussinesq方程弱解的爆破

本文主要研究一类耗散Boussinesq方程的初边值问题的弱解的有限时间爆破.我们主要研究了当初值落在位势井内时,弱解在有限时间爆破的充分必要条件,并给出爆破时间的下界估计.本文是对WANG和SU(2016)的文章的一个补充.     

广义两分量Camassa-Holm方程的柯西问题

研究了一个广义两分量Camassa-Holm方程的柯西问题,该模型可从经过线性切流的浅水波的理论机制中得出.文中讨论了该模型的爆破现象,建立了爆破发生时柯西问题的初始值满足的充分条件.同时研究了强解的持久和唯一连续性.     

带真空无磁扩散不可压磁流体方程柯西问题的局部适定性

该文讨论了在真空远场的密度条件下,二维不可压零磁耗散磁流体力学方程组柯西问题的局部适定性.在初始密度和磁场具有一定的衰减性时,证明了磁流体方程具有唯一的局部强解.当初值满足兼容性条件和适当的正则性条件时,该强解就是经典解.除此之外,文中还给出了一个仅与磁场有关的爆破准则.     

Wave breaking and global existence for the generalized periodic two-component Hunter–Saxton system

In this paper, we study the wave-breaking phenomena and global existence for the generalized two-component Hunter–Saxton system in the periodic setting. We first establish local well-posedness for the generalized two-component Hunter–Saxton system. We obtain a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions.     

On the Cauchy problem for the two-component Camassa�CHolm system

In this paper we establish the local well-posedness for the two-component Camassa?CHolm system in a range of the Besov spaces. We also derive a wave-breaking mechanism for strong solutions. In addition, we determine the exact blow-up rate of such solutions to the system.     

Blow-up for a weakly dissipative modified two-component Camassa–Holm system

In this paper, we study the Cauchy problem of a weakly dissipative modified two-component Camassa–Holm (MCH2) system. We first derive the precise blow-up scenario and then give several criteria guaranteeing the blow-up of the solutions. We finally discuss the blow-up rate of the blowing-up solutions.     

Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa–Holm system

We study the Cauchy problem of a weakly dissipative 2-component Camassa–Holm system. We first establish local well-posedness for a weakly dissipative 2-component Camassa–Holm system. We then present a global existence result for strong solutions to the system. We finally obtain several blow-up results and the blow-up rate of strong solutions to the system.     

Blow-up phenomena and global existence for the nonuniform weakly dissipative b-equation

We first establish the local well-posedness for the nonuniform weakly dissipative b-equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. We then study the blow-up phenomena and the long time behavior of the solutions. Two blow-up results are established for certain initial profiles. Moreover, two sufficient conditions for the decay of the solutions are presented.     

Global existence and blow-up phenomena for the weakly dissipative Novikov equation

In this paper, we consider the global existence and blow-up for the weakly dissipative Novikov equation. We firstly establish the local well-posedness for the weakly dissipative Novikov equation by Kato’s theorem. Then we present some blow-up results. Finally, we present the global existence of strong solutions to the weakly dissipative equation.     

Well-posedness,blow-up phenomena and persistence properties for a two-component water wave system

We first establish the local well-posedness for the Cauchy problem of a two-component water waves system in nonhomogeneous Besov spaces using the Littlewood–Paley theory. Then, we derive three new blow-up results for strong solutions to the system. Finally, we present two persistence properties for strong solutions to the system.     

On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation

In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.     

一类弱耗散Camassa-Holm 方程Cauchy问题在Besov 空间解的局部适定性

利用Littlewood-Paley 理论和输运方程解的先验估计, 在Besov 空间 中证明了一类弱耗散Camassa-Holm 方程Cauchy 问题解的局部适定性, 同时给出了解的能量估计及爆破准则.