Results 241 to 250 of about 36,044 (276)

Second Order Hyperbolic Equations with Small Nonlinearities

SIAM Journal on Applied Mathematics, 1978
A second order partial differential equation which describes the propagation of one-dimensional nonlinear waves in a bounded, inhomogeneous, dissipative medium is analyzed using the method of multiple scales. The conditions under which the oppositely traveling components of the nonlinear motion uncouple to first order are given.
Seymour, Brian R., Mortell, Michael P.
openaire   +2 more sources

Compact difference scheme for two‐dimensional fourth‐order nonlinear hyperbolic equation

Numerical Methods for Partial Differential Equations, 2020
High‐order compact finite difference method for solving the two‐dimensional fourth‐order nonlinear hyperbolic equation is considered in this article. In order to design an implicit compact finite difference scheme, the fourth‐order equation is written as
Qing Li, Qing Yang, Huanzhen Chen
semanticscholar   +1 more source

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

Existence and Uniqueness of Solutions to a Second Order Nonlinear Nonlocal Hyperbolic Equation

, 2001
Azmy Ackleh, Sergiu Aizicovici, Michael Demetriou, Simeon Reich   +3 more
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 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

Numerical methods for nonlinear second-order hyperbolic partial differential equations. II – Rothe’s techniques for 1-D problems

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

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

, 2021
S. A. Halim, Norafifi Najwa Wira, N. A. Hadi   +2 more
semanticscholar   +1 more source

Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly