Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, w...Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces HS（IR^2） with s 〉 1. Finally, an ill-posedness result is obtained in HS（IR^2） for s 〈 1.展开更多
In this paper, for any given observation time and suitable moving observation domains, the author establishes a sharp observability inequality for the Kirchhoff-Rayleigh plate like equation with a suitable potential i...In this paper, for any given observation time and suitable moving observation domains, the author establishes a sharp observability inequality for the Kirchhoff-Rayleigh plate like equation with a suitable potential in any space dimension. The approach is based on a delicate energy estimate. Moreover, the observability constant is estimated by means of an explicit function of the norm of the coefficient involved in the equation.展开更多
文摘Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
文摘Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces HS（IR^2） with s 〉 1. Finally, an ill-posedness result is obtained in HS（IR^2） for s 〈 1.
基金supported by the National Natural Science Foundation of China(Nos.10831007,60821091,60974035)
文摘In this paper, for any given observation time and suitable moving observation domains, the author establishes a sharp observability inequality for the Kirchhoff-Rayleigh plate like equation with a suitable potential in any space dimension. The approach is based on a delicate energy estimate. Moreover, the observability constant is estimated by means of an explicit function of the norm of the coefficient involved in the equation.
