The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonli...The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the abovementioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.展开更多
Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series o...Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.展开更多
This paper is the third part in a series of papers on adaptive finite elementmethods based on optimal error estimates for linear elliptic problems on the concavecorner domains. In this paper, a result is obtained. The...This paper is the third part in a series of papers on adaptive finite elementmethods based on optimal error estimates for linear elliptic problems on the concavecorner domains. In this paper, a result is obtained. The algorithms for error controlboth in the energy norm and in the maximum norm presented in part 1 and part 2 ofthis series arc based on this result.展开更多
We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the...We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.展开更多
基金Supported by the National Natural Science Foundation of China(10371073)
文摘The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the abovementioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.
文摘Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.
文摘This paper is the third part in a series of papers on adaptive finite elementmethods based on optimal error estimates for linear elliptic problems on the concavecorner domains. In this paper, a result is obtained. The algorithms for error controlboth in the energy norm and in the maximum norm presented in part 1 and part 2 ofthis series arc based on this result.
基金supported by National Natural Science Foundation of China (Grant No. 10871187)supported by the Science Research Program from the Education Department of Heilongjiang Province (Grant No. 11551137)
文摘We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.
