带逆平方势的非线性Schrdinger方程的阻尼影响

Effect of Damping for Nonlinear Schrdinger Equation with Inverse Square Potential

研究一类带逆平方势的阻尼非线性Schrdinger方程,此方程相对论分子物理中有磁性的粒子捕获电子的现象.物理上,阻尼通常弱化系统爆破.从数学上探究分析阻尼对系统爆破的精确影响.对于临界情形,建立一个产生爆破解的阻尼门槛.对于超临界情形,导出一个产生爆破解的阻尼区间.

This work is to concern the damped nonlinear Schrdinger equation with inverse square potential,which models the process of an electron being captured by polar molecules in non-relativistic molecular physics. We are interested in the effect of the damping in this system. In physics,damping usually weakens the blowup of systems. We analyze and explore the exact effect of the damping in the view of mathematics. For the critical case,a threshold of the damping is established to derive the blowup solution. For the supercritical case,an interval of the damping is constructed to yield the blowup solution.