Results 11 to 20 of about 36,044 (276)

Propagation of c°° regularity for fully nonlinear second order strictly hyperbolic equations in two variables [PDF]

Transactions of the American Mathematical Society, 1985
It is shown that if u u is a C 3 {C^3} solution of a fully nonlinear second order strictly hyperbolic equation in two variables, then u u is C ∞ {C^\infty } at a point m m as soon as it is
P. Godin
semanticscholar   +4 more sources

Higher-order single-step fully discrete approximations for nonlinear second-order hyperbolic equations

Computers & Mathematics with Applications, 1986
Error estimates are proved for finite element approximations to the solution of the initial-value problem \[ u_{tt}=\sum^{n}_{j,k=1}\partial /\partial x_ j(a_{jk}(x,t,u)\partial u/\partial x_ k)-a_ 0(t,x\quad,u)u+f(x,t,u)\quad in\quad \Omega \times [0,\tau], \] \(u=0\) in \(\partial \Omega \times [0,\tau]\), \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in ...
L. Bales
semanticscholar   +5 more sources

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Journal of the Egyptian Mathematical Society, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Navnit Jha, R. K. Mohanty
semanticscholar   +4 more sources

High order difference schemes for the system of two space second order nonlinear hyperbolic equations with variable coefficients

Journal of Computational and Applied Mathematics, 1996
The authors develop an implicit difference scheme for a system of two-space second-order nonlinear hyperbolic equations with variable coefficients and mixed derivatives. A number of numerical experiments is performed for illustration of the proposed techniques.
R. K. Mohanty, M. K. Jain, K. George
semanticscholar   +3 more sources

Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations

Computers & Mathematics with Applications, 1988
In an earlier paper [ibid. 12A, 581-604 (1986; Zbl 0596.65079)] the author considered the problem: \[ (1)\quad u_{tt}=\sum^{N}_{j,k=1}\partial /\partial x_ j[a_{j_ k}(x,t,u)\partial u/\partial x_ k]-a_ 0(x,t,u)u+f(x,t,u,u_ t,\nabla u) \] u\(=0\) in \(\Omega\) \(\times [0,\tau]\) \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in \(\Omega\), where \(\Omega\) is ...
L. Bales
semanticscholar   +4 more sources

A Two-Grid Finite Element Method for a Second-Order Nonlinear Hyperbolic Equation [PDF]

Abstract and Applied Analysis, 2014
We present a two-grid finite element scheme for the approximation of a second-order nonlinear hyperbolic equation in two space dimensions. In the two-grid scheme, the full nonlinear problem is solved only on a coarse grid of sizeH. The nonlinearities are expanded about the coarse grid solution on the fine gird of sizeh.
Chen, Chuanjun, Liu, Wei, Zhao, Xin
openaire   +6 more sources

Stability of Nonhyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation [PDF]

Journal of Difference Equations, 2015
This is a continuation part of our investigation in which the second order nonlinear rational difference equation xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1), n=0,1,2,…, where the parameters A≥0 and B, C, α, β, γ are positive real numbers and the initial conditions x-1, x0 are nonnegative real numbers such that A+Bx0+Cx-1>0, is considered.
S. Atawna, R. Abu-Saris, E. S. Ismail, I. Hashim   +3 more
openaire   +3 more sources

About the $C^\infty$-well-posedness of fully nonlinear weakly hyperbolic equations of second order with spatial degeneracy [PDF]

Advances in Differential Equations, 1997
M. Dreher, M. Reissig
semanticscholar   +5 more sources

A Novel Nonlinear Second Order Hyperbolic Partial Differential Equation-Based Image Restoration Algorithm With Directional Diffusion [PDF]

IEEE Access, 2020
Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE model based on directional diffusion for image restoration. This hyperbolic PDE restoration model can simply diffuse along the edge's tangential direction in the ...
Shuaijie Li, Zhanjiang Zhi
openaire   +3 more sources

The Cauchy problem in abstract Gevrey spaces for a nonlinear weakly hyperbolic equation of second order [PDF]

Hokkaido Mathematical Journal, 1994
The authors investigate the existence of local solutions to the abstract Cauchy problem: \[ (1)\quad u''+ A(t)u= f(t, u(t)), \qquad\quad (2)\quad u(0)= u_ 0, \quad u'(0)= u_ 1, \] in Hilbert space \(H\), where \(A(t)\) is a nonnegative unbounded operator.
D'ANCONA, Piero, MANFRIN, Renato
openaire   +4 more sources