Results 251 to 260 of about 122,957 (282)

Numerical methods for nonlinear second-order hyperbolic partial differential equations. I. Time-linearized finite difference methods for 1-D problems

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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First Darboux problem for nonlinear hyperbolic equations of second order

Mathematical Notes, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
O. M. Dzhokhadze, S. Kharibegashvili
semanticscholar   +2 more sources

Singularities of solutions for nonlinear hyperbolic equations of second order

, 2000
We consider the Cauchy problem for nonlinear hyperbolic partial differential equations of second order. Then the Cauchy problem does not generally admit a classical solution in the large, that is to say, singularities generally appear in finite time. The typical example of singularity is “shock wave”.
M. Tsuji
semanticscholar   +2 more sources

Reduction of Nonlinear Wave Equations to a Second-Order Quasi-linear Hyperbolic System

, 2017
As stated before, this book is concerned with the Cauchy problem of nonlinear wave equations with small initial data.
Tatsien Li, Yi Zhou
semanticscholar   +2 more sources

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

International Journal of Bifurcation and Chaos, 2015
If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a ...
Liangliang Li, Yu Huang, Goong Chen, Tingwen Huang   +3 more
semanticscholar   +3 more sources

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.
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Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms

Journal of Computational Physics, 2023
We consider the approximation of a class of dynamic partial differential equations (PDEs) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the nonlinear Klein ...
Yanxia Qian, Yongchao Zhang, Yunqing Huang, Suchuan Dong   +3 more
semanticscholar   +1 more source

Tangent interaction of co-normal waves for second order full nonlinear strictly hyperbolic equations

Nonlinear Analysis: Theory, Methods & Applications, 1992
Let \(u(x)\) be a solution of a full nonlinear strictly hyperbolic equation on \(\Omega\subset \mathbb{R}^ 3\) and let \(\Sigma_ 1\) and \(\Sigma_ 2\) be characteristic surfaces being simply tangent along the line \(\Gamma\). Using the paradifferential calculus the authors give the regularity properties [similar to that in the paper of \textit{S ...
Yin Huicheng, Qiu Qingjiu
semanticscholar   +3 more sources

New trends in the theory of nonlinear weakly hyperbolic equations of second order

Nonlinear Analysis: Theory, Methods & Applications, 1997
Today we have a relatively complete overview over the theory of strictly hyperbolic equations. If we consider for example the linear strictly hyperbolic equation of second-order \[ u_{tt}- a(x, t)u_{xx}+ b(x, t)u_x+ c(x,t)u_t+ d(x,t)u= f(x, t),\tag{1} \] strictly hyperbolic means, that the bounded coefficient \(a= a(x,t)\) satisfies \(a(x,t)\geq C>0\).
P. D’Ancona, M. Reissig
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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