Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a c...Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.展开更多
This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational solutions.The authors first prove a sufficient condition for the existence of a bound on the degree of the p...This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational solutions.The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE.An AODE satisfying this condition is called noncritical.Then the authors prove that some common classes of low-order AODEs are noncritical.For rational solutions,the authors determine a class of AODEs,which are called maximally comparable,such that the possible poles of any rational solutions are recognizable from their coefficients.This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient.Finally,the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs,which is applicable to 78.54%of the AODEs in Kamke's collection of standard differential equations.展开更多
基金supported by the National Natural Science Foundation of China(Nos.91330202,11301089,91130004)Chinese Ministry of Education(No.20110071120001)the Programme of Introducing Talents of Discipline to Universities of China(No.B08018)
文摘Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.
基金supported by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant No.101.04-2019.06supported by the Austrian Science Fund(FWF)under Grant No.P29467-N32+1 种基金the UTD startup Fund under Grant No.P-1-03246the Natural Science Foundations of USA under Grant No.CF-1815108 and CCF-1708884。
文摘This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational solutions.The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE.An AODE satisfying this condition is called noncritical.Then the authors prove that some common classes of low-order AODEs are noncritical.For rational solutions,the authors determine a class of AODEs,which are called maximally comparable,such that the possible poles of any rational solutions are recognizable from their coefficients.This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient.Finally,the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs,which is applicable to 78.54%of the AODEs in Kamke's collection of standard differential equations.
