We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural ...We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact Rs, while for the nonconvex problem we show that it is path connected, Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.展开更多
In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we...In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we obtain the volume of the ball associated to Lα and prove the nonexistence for a second order evolution inequality which is relative to Lα.展开更多
文摘We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact Rs, while for the nonconvex problem we show that it is path connected, Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.
文摘In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we obtain the volume of the ball associated to Lα and prove the nonexistence for a second order evolution inequality which is relative to Lα.
