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1.
Conditions are derived for the linearizability via invertible maps of a system of n second-order quadratically semi-linear differential equations that have no lower degree lower order terms in them, i.e.,
for the symmetry Lie algebra of the system to be sl(n + 2, ℝ). These conditions are stated in terms of the coefficients of the equations and hence provide simple invariant criteria
for such systems to admit the maximal symmetry algebra. We provide the explicit procedure for the construction of the linearizing
transformation. In the simplest case of a system of two second-order quadratically semi-linear equations without the linear
terms in the derivatives, we also provide the construction of the linearizing point transformation using complex variables.
Examples are given to illustrate our approach for two- and three-dimensional systems. 相似文献
2.
This work deals with the relation between the numerical solutions of hyperbolic systems of conservation laws and the associated entropy evolution. An analysis of the continuum problem by means of variational calculus clearly emphasizes the consequences of the adopted reconstruction procedure on the induced entropy balance. A methodology is proposed that allows for a posterior local and global spurious entropy production estimates on the basis of an additional equation representing a discrete approximation to the entropy inequality. The problem of defining a consistent approximation of the numerical entropy flux is also addressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. © 1997 John Wiley & Sons, Ltd. 相似文献
3.
This paper investigates equation(1)in two cases:(i)P≡0,(ii)P(≠O)satisfies|P(t,x,y,z,ω)|≤(A |y| |z| |ω|)q(t),where q(t)is a nonnegative function of t.For case(i)the asymptotic stability in the large of the trivial solution x=0 is investigatedand for case(ii)the boundedness result is obtained for solutions of equation(1).Theseresults improve and include several well-known results. 相似文献
4.
Approximate symmetries have been defined in the context of differential equations and systems of differential equations. They
give approximately, conserved quantities for Lagrangian systems. In this paper, the exact and the approximate symmetries of
the system of geodesic equations for the Schwarzschild metric, and in particular for the radial equation of motion, are studied.
It is noted that there is an ambiguity in the formulation of approximate symmetries that needs to be clarified by consideration
of the Lagrangian for the system of equations. The significance of approximate symmetries in this context is discussed. 相似文献
5.
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping
time as terminal under the non-Lipschitz condition are obtained. The convergence of solutions and the continuous dependence
of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi-linear
elliptic type integro-differential equations is obtained.
Foundation item: the National Natural Science Foundation of China (79790130); the Foundation of Zhongshan University Front
Research
Biography: Situ Rong (1935 −) 相似文献
6.
Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow 下载免费PDF全文
In this paper, we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer systems. It is derived using the balance of the total energy in the complete network. The resulting system of equations contains, aside from hyperbolic conservation laws for the sewer network and algebraic relations for the coupling conditions, a system of ODEs governing the flow in the manholes. The manholes provide natural points for the interaction of the sewer system and the runoff on the urban surface modeled by shallow‐water equations. Finally, a numerical method for the coupled system is presented. In several numerical tests, we study the influence of the manhole model on the sewer system and the coupling with 2D surface flow. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
ONTHEBOUNDEDNESSANDTHESTABILITYRESULTSFORTHESOLUTIONOFCERTAINFOURTHORDERDIFFERENTIALEQUATIONSVIATHEINTRINSICMETHODCemilTUNC;A... 相似文献
8.
The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches. 相似文献
9.
Yu. A. Chirkunov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):213-219
An algorithm is proposed which allows all conservation laws for a system of differential equations to be to obtained from
its one zero-order conservation law for which the general rank of the Jacobi matrix is equal to the number of independent
variables of the system. The efficiency of the algorithm is shown by examples of the equations of gas dynamics, for which
new conservation laws are derived. For the equations considered, additional symmetry properties related to these conservation
laws are established.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 53–60, March–April, 2009. 相似文献