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1.
Global existence of weak discontinuous solutions to the Cauchy problem with small BV initial data for quasilinear hyperbolic systems 下载免费PDF全文
Libin Wang 《Mathematical Methods in the Applied Sciences》2015,38(5):966-979
In this paper, we study the Cauchy problem for quasilinear hyperbolic system with a kind of non‐smooth initial data. Under the assumption that the initial data possess a suitably small bounded variation norm, a necessary and sufficient condition is obtained to guarantee the existence and uniqueness of global weak discontinuous solution. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
Existence and convergence of Galerkin approximation for second order hyperbolic equations with memory term 下载免费PDF全文
Fardin Saedpanah 《Numerical Methods for Partial Differential Equations》2016,32(2):548-563
We study a second order hyperbolic initial‐boundary value partial differential equation (PDE) with memory that results in an integro‐differential equation with a convolution kernel. The kernel is assumed to be either smooth or no worse than weakly singular, that arise for example, in linear and fractional order viscoelasticity. Existence and uniqueness of the spatial local and global Galerkin approximation of the problem is proved by means of Picard's iteration. Then, spatial finite element approximation of the problem is formulated, and optimal order a priori estimates are proved by the energy method. The required regularity of the solution, for the optimal order of convergence, is the same as minimum regularity of the solution for second order hyperbolic PDEs. Spatial rate of convergence of the finite element approximation is illustrated by a numerical example. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 548–563, 2016 相似文献
3.
O. Jokhadze 《Georgian Mathematical Journal》1998,5(2):121-138
Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of
partial differential equations of first order are studied. A condition is given which enables one to reduce the system under
consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in
a certain class of functions if some conditions are fulfilled. 相似文献
4.
T. V. Zavrazhina 《Computational Mathematics and Mathematical Physics》2007,47(10):1622-1630
A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ?2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed. 相似文献