In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Sc...In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.展开更多
We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include...We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（40537034）
文摘In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.
文摘We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.
