Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and u...This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.展开更多
In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Pal...In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.展开更多
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
文摘This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.
基金supported by National Natural Science Foundation of China(Grant Nos.10771219 and 11071092)the PhD Specialized Grant of the Ministry of Education of China(Grant No.20110144110001)
文摘In this paper,a system of elliptic equations is investigated,which involves Hardy potential and multiple critical Sobolev exponents.By a global compactness argument of variational method and a fine analysis on the Palais-Smale sequences created from related approximation problems,the existence of infinitely many solutions to the system is established.
