In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Th...In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Then,a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite.Finally,the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.展开更多
This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f...This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.展开更多
In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in ...In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in the unit ball in Rn, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.展开更多
基金part of the project(No.PID2019-105118GB-I00),funded by the Spanish Ministry of Science,Innovation and Universities and FEDER“A way to make Europe”。
文摘In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Then,a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite.Finally,the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.
基金in part supported by NSERC of Canada and the Finnish Cultural Foundation
文摘This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.
文摘In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in the unit ball in Rn, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.
