This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands.In this work,we employ the variational limiting equilibrium procedure to theoretically determ...This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands.In this work,we employ the variational limiting equilibrium procedure to theoretically determine the slope stability of coral reefs covered with hard reef shells as a result of horizontal wave loads.A reasonable functional is proposed and its extremum is calculated based on the conservation of energy.Then,we deduce the stability factor Ns of coral reefs under combined vertical self-gravity and horizontal wave loads,which is consistent with the published results.We compare some classic examples of homogeneous slopes without hard shells in order to analyze the accuracy of results generated by this variational procedure.The variational results are accurate and reliable according to the results of a series of detailed calculations and comparisons.Simultaneously,some other influence parameters on the reef stability,including the top-layer tensile strength of coral reef,the amplitude of wave loading,and the tensile crack,are calculated and discussed in detail.The analysis results reveal that the existence of a hard reef shell could enhance the stability of reef slope and that there is a nonlinear relationship between the stability factor Ns,the shear strength,and the thickness Ds of the covered coral reef shell.Furthermore,the emergence of top-layer tensile cracks on the coral reefs reduces their stability,and the action of horizontal wave loads greatly decreases the stability of coral reefs.Thus,the hard shell strength and its thickness Ds,surface tensile crack,and wave loading require more careful attention in the field of practical engineering.展开更多
This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0...This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.展开更多
Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak...Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.展开更多
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro-posed in the paper,with the help of minimizing some kinds of quadratic functional in calculus of variation.At first,th...A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro-posed in the paper,with the help of minimizing some kinds of quadratic functional in calculus of variation.At first,the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation.Then theoretical properties related with the solution are derived,especially for its existence,uniqueness and optimal approximation.And then the computational method of the solution is discussed,and its expression is exhibited under the case that all boundaries are spheres.Finally an arithmetic example about EGM96 gravity field model is given,and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data.In all,the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form,but also has strict mathematical basements.展开更多
The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation o...The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.展开更多
基金the Project of National Science and Technology Ministry(No.2014BAB16B03)the National Natural Science Foundation of China(No.51679224)。
文摘This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands.In this work,we employ the variational limiting equilibrium procedure to theoretically determine the slope stability of coral reefs covered with hard reef shells as a result of horizontal wave loads.A reasonable functional is proposed and its extremum is calculated based on the conservation of energy.Then,we deduce the stability factor Ns of coral reefs under combined vertical self-gravity and horizontal wave loads,which is consistent with the published results.We compare some classic examples of homogeneous slopes without hard shells in order to analyze the accuracy of results generated by this variational procedure.The variational results are accurate and reliable according to the results of a series of detailed calculations and comparisons.Simultaneously,some other influence parameters on the reef stability,including the top-layer tensile strength of coral reef,the amplitude of wave loading,and the tensile crack,are calculated and discussed in detail.The analysis results reveal that the existence of a hard reef shell could enhance the stability of reef slope and that there is a nonlinear relationship between the stability factor Ns,the shear strength,and the thickness Ds of the covered coral reef shell.Furthermore,the emergence of top-layer tensile cracks on the coral reefs reduces their stability,and the action of horizontal wave loads greatly decreases the stability of coral reefs.Thus,the hard shell strength and its thickness Ds,surface tensile crack,and wave loading require more careful attention in the field of practical engineering.
文摘This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.
文摘Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.
基金Supported by the National Natural Science Foundation of China(Grant No.40374001)
文摘A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro-posed in the paper,with the help of minimizing some kinds of quadratic functional in calculus of variation.At first,the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation.Then theoretical properties related with the solution are derived,especially for its existence,uniqueness and optimal approximation.And then the computational method of the solution is discussed,and its expression is exhibited under the case that all boundaries are spheres.Finally an arithmetic example about EGM96 gravity field model is given,and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data.In all,the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form,but also has strict mathematical basements.
基金supported in part by grant from IPM(No.89350020)
文摘The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.
