具变指数非线性拟抛物方程弱解的2个性质

Two Properties of Weak Solutions for a Nonlinear Pseudoparabolic Equation with Variable Exponent

关注一类具变指数非线性拟抛物方程初边值问题弱解的渐近行为和弱解支集的单调性问题.利用泛函的凸性,得到弱解的能量等式,根据此结果并使用Poincaré不等式和Hlder不等式,讨论了具变指数非线性拟抛物方程弱解的渐近行为.此外,使用Steklov均值性质,导出弱解的比较原理,在一维情形中,利用该比较原理,证明了此拟抛物方程弱解支集的单调性.

The asymptotic behavior and monotonicity support of weak solutions to the initial-boundary value problem for a class of nonlinear pseudoparabolic equation with variable exponent are considered. The energy equality of weak solutions is obtained by using convexity of functional. By this and Poincaré＇s and Hlder＇s inequalities the asymptotic behavior of weak solutions to the nonlinear pseudoparabolic equation with variable exponent is discussed.The comparison principle is obtained by using of Steklov mean property of weak solutions. By this comparison principle,the monotonicity support of weak solutions is proved in 1-dimension.