论文标题
潜力在某些进化方程的l^{2}估计中的作用
A role of potential on L^{2}-estimates for some evolution equations
论文作者
论文摘要
在此PAPWE中，我们考虑了在溶液本身的L^{2} - 质量上，波动方程的潜力的有效作用。在自由波方程式中，众所周知，解决方案本身的l^{2} - 通常会在一个和二维情况下生长到无穷大（随着时间的时间流向无穷大），但是，通过在相当宽敞的条件下添加电势，可以控制生长特性，以使生长特性获得L^{2} - 结合。该想法也可以应用于具有潜力的阻尼波方程，以获取快速能量，l^{2}衰减会导致低维情况，这是长时间开放的。还可以研究在具有电势的热和板方程的应用。在本文中，低维情况是主要目标。
In this papwe we consider an effective role of the potential of the wave equations with/without damping on the L^{2}-estimate of the solution itself. In the free wave equation case it is known that the L^{2}-norm of the solution itself generally grows to infinity (as time goes to infinity) in the one and two dimensional cases, however, by adding the potential with quite generous conditions one can controle the growth property to get the L^{2}-bounds. This idea can be also applied to the damped wave equations with potential in order to get fast energy and L^{2} decay results in the low dimensional case, which are open for a long period. Applications to heat and plate equations with a potential can be also studied. In this paper the low dimensional case is a main target.
