一类二阶拟线性瞬态方程组的Phragmen-Lindelof型二择性结果

Phragmen-Lindelof Type Alternative Results for a Class of Second Order Quasilinear Transient Equations

考虑一类定义在三维半无穷柱体上的拟线性方程组,其中假设方程的解在柱体的有限端满足非齐次条件,在柱体的侧面上满足零边界条件.通过对非线性项进行限制,利用微分不等式技术,给出该方程的解在3种不同柱体上的二择一定理,并在衰减的情形下给出全能量的上界.

We considered a class of quasilinear equations defined on a three-dimensional semi infinite cylinder,in which the solutions of the equations were assumed to satisfy the nonhomogeneous condition at the finite end of the cylinder and the zero boundary condition at the side of the cylinder.By limiting the nonlinear terms and using the differential inequality technique,we gave the alternative theorem of the solutions of the equations on three different cylinders,and gave the upper bound of total energy in the case of decay.