A Quasilinear Parabolic System with Nonlocal Boundary Conditions and Localized Sources

This paper investigates the properties of solutions to a quasilinear parabolicsystem with nonlocal boundary conditions and localized sources. Conditions for theexistence of global or blow-up solutions are given. Global blow-up property and blow-up rate estimates are also derived.     

Properties of positive solutions to a nonlinear parabolic problem

This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.     

一类生物捕食模型解的整体存在性和爆破性

研究了一类具有捕食速率的生物捕食模型解整体存在性和爆破性,利用反映扩散方程组的比较原理,通过构造自相似形式的上下解,得到了模型的解的整体存在和爆破条件.     

多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象

利用拟线性双曲型方程组极值原理,改进了HSIAO Ling和D.Serre得到的关于多孔介质中可压缩流体力学方程组解的存在性结果,给出了其Cauchy问题的一个关于经典解整体存在和破裂的完整结果．这些结果说明强耗散有助于“小”解的光滑性．     

Blow-up of solutions to a parabolic system with nonlocal source

This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods.     

Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions

This paper deals with the global existence and blow-up of positive solutions to the systems: u_t = ∇(u^∇u) + u¹ + v^a v_t = ∇(v^n∇v) + u^b + v^k in B_R × (0, T) \frac{∂u}{∂η} = u^αv^p, \frac{∂v}{∂η} = u^qv^β on S_R × (0, T) u(x, 0) = u_0(x), v(x, 0} = v_0(x) in B_R We prove that there exists a global classical positive solution if and only if l ≤ l, k ≤ 1, m + α ≤ 1, n + β ≤ 1, pq ≤ (1 - m - α)(1 - n - β),ab ≤ 1, qa ≤ (1 - n - β) and pb ≤ (1 - m - α).     

一类GBBM方程的柯西问题

研究一类非线性拟抛物方程的柯西问题.首先利用与原方程等价的积分方程以及压缩映像原理得到了问题的局部W~(k,p)解的存在性,而后在某些假设下得到了问题W~(k,p)解的整体存在性,最后利用凸性方法得到了解的有限时间内爆破.     

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.     

带有局部源的非局部扩散方程组的Fujita现象

本文研究了一类带有局部源的非局部扩散系统$u_t=J*u-u+a(x)v^{p}$, $v_t=J*v-v+a(x)u^q$的柯西问题,首先根据是否存在全局解建立了Fujita曲线$(pq)_c=1+max {p+1,q+1}$,也即证明了:如果$1(pq)_c$时,则既存在全局解,也存在非全局解.然后我还根据初始值在无穷远处的衰减率建立了第二临界曲线.     

弱耗散非线性浅水波方程周期柯西问题

建立了弱耗散非线性浅水波方程的局部适定性,对于不同的初始值,我们分别得到了解的整体存在性和解的爆破。     

Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation

In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equation u_{tt} + k_1u_{xxxx} + k_2u_{xxxxt} + g(u_{xx})_{xx} = f(x, t) are proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.