Results 261 to 270 of about 122,957 (282)

Oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve

Acta Mathematica Sinica, English Series, 2011
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained ...
G. Wen
semanticscholar   +2 more sources

Long time effects of nonlinearity in second order hyperbolic equations

Communications on Pure and Applied Mathematics, 1986
This is an expository paper based on a talk given by the author on October 21, 1985. The author considers initial value problems for the quasilinear equation \[ u_{tt}-2b_ i(u')u_{tx_ i}- a_{ik}(u')u_{x_ ix_ i}=0,\quad u'=(u_ t,u_{x_ i},...,u_{x_ n}) \] and describes some of the methods used to discuss existence of solutions for large t.
openaire   +2 more sources

Propagation of analytic regularity for analytic fully nonlinear second order strictly hyperbolic equations in two variables

Communications in Partial Differential Equations, 1986
Etude de la propagation de la regularite pour les equations a deux variables, analytiques strictement hyperboliques completement non lineaires du second ...
P. Godin
semanticscholar   +2 more sources

A solvability result for a nonlinear weakly hyperbolic equation of second order

Nonlinear Differential Equations and Applications NoDEA, 1995
The author considers the Cauchy problem \[ u_{tt} - u^{2k} \sum^n_{i,j = 1} a_{ij} (t,x,u) u_{x_i x_j} = f(t,x,u,u_t), \quad u (0,x) = \Phi (x),\;u_t(0,x) = \Psi (x), \] where \(\Phi\), \(\Psi \in C_0^\infty (\mathbb{R}^n)\), \(k \in \mathbb{N}\), \(a_{ij} = a_{ji}\), \(f\) are \(C^\infty\)-functions, \(f(t,x,0,0) = 0\), and \[ \sum^n_{i,j = 1} a_{ij} \
openaire   +2 more sources

Second-order finite-volume schemes for a non-linear hyperbolic equation: error estimate

Mathematical Methods in the Applied Sciences, 2000
Second-order finite volume schemes for multidimensional nonlinear hyperbolic equations one derived and studied. The main result is an error estimate for the approximation to the entropy solution of the equation. A discrete entropy inequality is introduced and proved under natural assumptions on the problem. An error estimate of order \(h^{n/k}\) (\(h\)
openaire   +2 more sources

On the application of mixed finite element method for a strongly nonlinear second-order hyperbolic equation

Korean Journal of Computational & Applied Mathematics, 1998
The authors consider the initial-boundary value problem for a nonlinear hyperbolic equation of second order in flux formulation, \[ \text{grad }p+ \underline b(\underline u)= \underline O\quad\text{in }\Omega\times (0,T], \] \[ p_{tt}+ \text{div }\underline u= f\quad\text{in }\Omega\times (0,T], \] where \(p\), \(f\) are scalars and \(\underline u\), \(
Jiang, Ziwen, Chen, Huanzhen
openaire   +2 more sources

On a Certain Class of Hyperbolic Equations with Second-Order Integrals

Journal of Mathematical Sciences, 2021
A. V. Zhiber, A. M. Yur’eva
semanticscholar   +2 more sources

Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space

Topological Methods in Nonlinear Analysis
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for their finding are obtained in the case when the operator in linear part of the problem hasn't inverse and can have ...
openaire   +1 more source

Image Denoising using Modified Diffusion Functions on Nonlinear Second-Order Hyperbolic Model

, 2021
S. A. Halim, N. N. Wira, N. A. Hadi
semanticscholar   +1 more source

Second- and Third-Order Noncentered Difference Schemes for Nonlinear Hyperbolic Equations

, 1973
R. F. Warming, P. Kutler, H. Lomax
semanticscholar   +1 more source