Under the assumption that the forcing function of a neutral delay difference equation is exponentially decaying, we find sufficient conditions for all solutions of this equation to be exponentially decaying. Applicati...Under the assumption that the forcing function of a neutral delay difference equation is exponentially decaying, we find sufficient conditions for all solutions of this equation to be exponentially decaying. Applications of our results are obtained for a class of parabolic type partial difference equations.展开更多
In this paper, we shall study the solutions of functional equations of the formΦ=∑α∈Zsa（α）Φ（M.-α）where is an r × 1 column vector of functions on the s-dimensional Euclidean space,a ：= （a（a））α∈Zs...In this paper, we shall study the solutions of functional equations of the formΦ=∑α∈Zsa（α）Φ（M.-α）where is an r × 1 column vector of functions on the s-dimensional Euclidean space,a ：= （a（a））α∈Zs is an exponentially decaying sequence of r × r complex matrices called refinement mask and M is an s × s integer matrix such that limn∞ M-n =0. We axe interested in the question, for a mask a with exponential decay, if there exists a solution ~ to the functional equation with each function φj, j = 1,... ,r, belonging to L2（Rs） and having exponential decay in some sense？ Our approach will be to consider the convergence of vector cascade algorithms in weighted L2 spaces. The vector cascade operator Qa,M associated with mask a and matrix M is defined by展开更多
Consider the following difference equation with continuous argumentsy(f) = p(t)y(t-τ) + q(t)y(t-δ(t)) + R(t).Under the assumption that the forcing function R(t) is exponentially decaying, we obtain sufficient condi...Consider the following difference equation with continuous argumentsy(f) = p(t)y(t-τ) + q(t)y(t-δ(t)) + R(t).Under the assumption that the forcing function R(t) is exponentially decaying, we obtain sufficient conditions for all solutions of this equation to be exponentially decaying,these conditions are also necessary for some special cases.展开更多
A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensur...A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensured from theoretical analysis,and this is the theoretical foundation of the critical point method for the measurement of corrosion current of metals.The comparison of the corrosion currents measured by the critical point and static methods for the system of 321 stainless steel in 0.5N HCI+0.5N NaCI solution at static state shows that the results agree very well.Finally.the tran- sient corrosion currents of 321 stainless steel in 0.5N HCI+0.5N NaCl solution at different strain level are listed.展开更多
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.展开更多
文摘Under the assumption that the forcing function of a neutral delay difference equation is exponentially decaying, we find sufficient conditions for all solutions of this equation to be exponentially decaying. Applications of our results are obtained for a class of parabolic type partial difference equations.
基金Supported by National Natural Science Foundation of China(Grant Nos.11101120, 11171299 and 11001247)Fundamental Research Funds for the Central Universities
文摘In this paper, we shall study the solutions of functional equations of the formΦ=∑α∈Zsa（α）Φ（M.-α）where is an r × 1 column vector of functions on the s-dimensional Euclidean space,a ：= （a（a））α∈Zs is an exponentially decaying sequence of r × r complex matrices called refinement mask and M is an s × s integer matrix such that limn∞ M-n =0. We axe interested in the question, for a mask a with exponential decay, if there exists a solution ~ to the functional equation with each function φj, j = 1,... ,r, belonging to L2（Rs） and having exponential decay in some sense？ Our approach will be to consider the convergence of vector cascade algorithms in weighted L2 spaces. The vector cascade operator Qa,M associated with mask a and matrix M is defined by
文摘Consider the following difference equation with continuous argumentsy(f) = p(t)y(t-τ) + q(t)y(t-δ(t)) + R(t).Under the assumption that the forcing function R(t) is exponentially decaying, we obtain sufficient conditions for all solutions of this equation to be exponentially decaying,these conditions are also necessary for some special cases.
文摘A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensured from theoretical analysis,and this is the theoretical foundation of the critical point method for the measurement of corrosion current of metals.The comparison of the corrosion currents measured by the critical point and static methods for the system of 321 stainless steel in 0.5N HCI+0.5N NaCI solution at static state shows that the results agree very well.Finally.the tran- sient corrosion currents of 321 stainless steel in 0.5N HCI+0.5N NaCl solution at different strain level are listed.
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.
