共查询到10条相似文献,搜索用时 62 毫秒
1.
The local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime was proved in Duruk Mutlubaş (2013). In this paper, we correct the mistake made in the proof of the main result and give the appropriate assumptions and corresponding results. 相似文献
2.
N. Duruk Mutlubaş 《Nonlinear Analysis: Real World Applications》2013,14(5):2022-2026
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime. 相似文献
3.
We consider three kind of oscillatory properties of the solutions to semilinear degenerate hyperbolic equations. Several sufficient conditions for the oscillation or non-oscillation are presented. In particular, they give us the positivity of the solutions for semilinear hyperbolic equations degenerating at initial point in one space dimension. Moreover we establish a few oscillatory conditions for the solutions of the mixed problem reduced to in one space dimension. 相似文献
4.
In the present work a fourth order accuracy decomposition scheme is constructed for a multidimensional nonhomogeneous hyperbolic equation on the basis of rational splitting of cosine operator-function. The main operator of the equation is self-adjoint and positive definite. The stability of the constructed scheme is shown and the error of the approximate solution is estimated. On the basis of the constructed scheme, numerical calculations of test problems for three-dimensional case are carried out. The numerical results obtained verify that the suggested scheme has a fourth order accuracy. 相似文献
5.
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4]. 相似文献
6.
V. M. Gordienko 《Siberian Mathematical Journal》2009,50(1):14-21
Some relation along an additional characteristic is constructed for a class of Friedrichs hyperbolic systems to which the wave equation is reduced. The statement is proven about preservation of a vortex. The conditions are stated for the solutions to Friedrichs hyperbolic systems of this class to remain solutions to the initial wave equation. 相似文献
7.
Britton Chang Anne Greenbaum Eric Machorro 《Numerical Linear Algebra with Applications》2011,18(1):141-154
In this paper, we prove that the piecewise bilinear Petrov‐Galerkin discretization for the mono‐directional neutron transport equation described in (J. Comput. Phys. 1986; 64 :96–111) is convergent and second‐order accurate, provided that the true solution to the problem has continuous partial derivatives of all orders up through three. We do this by giving a bound on the 2‐norm of the inverse of the system matrix that is independent of the mesh size. This shows that the global error is of the same order as the local truncation error. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
8.
1IntroductionThepurposeofthispaperistoextendsomeoscilationresultsofthepapers[1,2]totheneutralhyperbolicdiferentialequationoft... 相似文献
9.
Taeko Yamazaki 《Mathematical Methods in the Applied Sciences》2009,32(15):1893-1918
We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear hyperbolic equation of Kirchhoff type with dissipation weak in time. The purpose of this paper is to give time‐decay convergence estimates of the difference between the solutions of the hyperbolic equation above and those of the corresponding parabolic equation, together with the unique existence of the global solutions of the hyperbolic equation above. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
对非齐次线性退化富有组的柯西问题,证明了在奇性的发生处解的C0模必趋于无穷。 相似文献