The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve ...The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.展开更多
This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and t...In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and the void fraction is used.There are several difficulties in problem solving,and the solutions are provided.Firstly,the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error.While the void fraction inequality constraint is considered by using the hard constraint with the max-min function.Secondly,to avoid the fluctuation of the boundary value problems,the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided.Lastly,for avoiding the trivial solution the limitation for the mean value of the void fraction is applied.The results are validated against existing data,and both the incompressible and compressible lubricant are considered.Good agreement can be found for both the domain and domain boundaries.展开更多
基金The author is supported in part by NNSF of China and Monbusho Scholarship of Japan.
文摘The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.
文摘This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
基金the funding from Anhui University of Science and Technology(No.2022yjrc15)the Key Project of National Natural Science Foundation of China(Nos.U21A20125 and U21A20122)+1 种基金the Key Research and Development Projects of Anhui Province(No.2022a05020043)the National Natural Science Foundation of China(Nos.51805410 and 51804007).
文摘In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and the void fraction is used.There are several difficulties in problem solving,and the solutions are provided.Firstly,the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error.While the void fraction inequality constraint is considered by using the hard constraint with the max-min function.Secondly,to avoid the fluctuation of the boundary value problems,the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided.Lastly,for avoiding the trivial solution the limitation for the mean value of the void fraction is applied.The results are validated against existing data,and both the incompressible and compressible lubricant are considered.Good agreement can be found for both the domain and domain boundaries.
