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.     

R~2中具有趋化性的抛物-椭圆系统的解的性态分析

在二维空间中讨论了一个抛物-椭圆系统,而该系统来源于生物学中的趋化性模型.主要在Sobolev空间的框架下讨论了解的全局存在性与解的爆破性质,得出结论该系统存在一个门槛值,而该值决定了解全局存在或者发生爆破.最后利用利李亚普诺夫函数给出了定理的证明并得出结论.     

具非局部源退化抛物型方程组的一致爆破模式

考虑带有齐次Dirichlet边界条件且具有非局部源项的退化抛物型方程组正解的爆破性质. 在适当条件下, 建立了该问题解的局部存在性并证明解在有限时刻爆破, 此外,还导出了解的两个分量同时爆破的必要条件, 并得到了该问题解的一致爆破模式.     

一类具非局部源抛物型方程组解的一致爆破性质

考虑带有齐次Dirichlet边界条件,具非局部源项的半线性抛物型方程组正解的爆破性质,首先给出了该问题的解在有限时刻爆破的充分条件,以及解的两个分量同时爆破的必要条件,并建立了解的一致爆破模式.     

带有非线性局部化反应源项的抛物型方程组解的一致爆破模式与边界层

考虑带有齐次Dirichlet边界条件, 反应项为非线性局部化源项的半线性抛物型方程组解的爆破性质. 首先给出了该问题的古典解在有限时刻爆破的充分条件, 以及解的两个分量同时爆破的必要条件和一个充分条件, 然后得到了解的内部一致爆破模式, 最后描述了爆破解在边界层上的渐近行为.     

半线性抛物型方程组解的整体存在性与爆破速率估计

研究了具有非线性热源的半线性抛物型方程组的齐次neumann问题解的爆破性质.利用上下解方法得到了解整体存在的条件与爆破条件,并利用FriedmannMcleod方法建立了爆破速率估计.     

一类含非局部源的非线性退化扩散方程解的爆破性质

研究了一类带非局部源的非线性退化抛物型方程.在一定条件下,证得方程的解在有限时刻爆破且爆破点集为整个区域.积分方法被用来研究解的爆破性质.     

带有自由边界的反应扩散系统解的整体存在与爆破（英文）

本文研究一类带耦合非线性反应项的反应扩散系统的自由边界问题.为简便起见,假设条件和解都是径向对称的.首先,利用压缩映射定理,给出正解的局部存在性和唯一性.然后,考虑解的爆破性质和长时间行为.     

一类弱耗散双组份Hunter-Saxton系统的爆破与爆破率

研究了一类周期弱耗散双组份Hunnter-Saxton系统的爆破现象.首先,给出了此类Hunnter-Saxton系统解的局部适定性及其精确的爆破机制;其次,证明了在一定的初始值下Hunnter-Saxton系统强解的几个爆破结果;最后,给出了HunnterSaxton系统强解的爆破率.     

非均匀介质中Zakharov系统的位力奇性解

研究非均匀介质中Zakharov系统的位力奇性解.该系统描述了静电势与等离子密度在静电极限意义下的相互作用.一方面,利用位力恒等式,在c₀=+∞时证明了所研究的Zakharov系统的有限时间爆破结果.另一方面,通过建立局部的位力恒等式并利用关于时间的Lyapunov函数的存在性,在00<+∞时得到了所研究的Zakharov系统具负能量的径向对称解的爆破结果.     

Exponential Decay of Energy for a Logarithmic Wave Equation

In this paper we consider the initial boundary value problem for a class of logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the logarithmic wave equation with linear damping and some suitable initial data. The results extend the early results.     

Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as for one-dimensional case.     

有限初始能量的相对论欧拉方程组光滑解的爆破

在初始资料的某些限制下证明有限初始能量的相对论欧拉方程组柯西问题光滑解的爆破.该文的爆破条件不需要初始资料具有紧支集,部分补充了Pan和Smoller的经典爆破结果(2006).     

Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schrödinger equation. Using these estimates, we obtain some new results related to nonlinear problems, including small data scattering and large data LWP for the nonlinear Schrödinger and wave equations with radial critical initial data and the well-posedness theory for the fractional order Schrödinger equation in the radial case.     

Almost everywhere well-posedness of continuity equations with measure initial data

The aim of this Note is to present some new results concerning “almost everywhere” well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in Ambrosio et al. [4], together with some application to the semiclassical limit of the Schrödinger equation.     

Existence results for viscous polytropic fluids with vacuum

We consider the full Navier-Stokes equations for viscous polytropic fluids with nonnegative thermal conductivity. We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover our results hold for both bounded and unbounded domains.     

Initial value problems for creeping flow of Maxwell fluids

We consider the flow of nonlinear Maxwell fluids in the unsteady quasistatic case, where the effect of inertia is neglected. We study the well-posedness of the resulting PDE initial-boundary value problem locally in time. This well-posedness depends on the unique solvability of an elliptic boundary value problem. We first present results for the 3D case with sufficiently small initial data and for a simple shear flow problem with arbitrary initial data; after that we extend our results to some 3D flow problems with large initial data.We solve our problem using an iteration between linear subproblems. The limit of the iteration provides the solution of our original problem.     

Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions

Of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions. Under some suitable hypotheses, we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations. Moreover, an example is given to illustrate our results.     

Blow-up of smooth solutions to the compressible magnetohydrodynamic flows

In this paper, we prove the blow-up phenomena of smooth solutions to the Cauchy problem for the full compressible magnetohydrodynamic equations and isentropic compressible magnetohydrodynamic equations with constant and degenerate viscosities under some restrictions on the initial data. In particular, our results do not require that the initial data have compact support or contain vacuum in any finite region.     

Numerical Solution of Time Fractional Burgers Equation by Cubic B-spline Finite Elements

Mediterranean Journal of Mathematics - We present some numerical examples which support numerical results for the time fractional Burgers equation with various boundary and initial conditions...