Results 291 to 300 of about 159,157 (335)

First-order Equations and Hyperbolic Second-order Equations

1999
The concept of a characteristic curve for a second-order equation was introduced in Chapter 1, and led to a classification of these equations. When the characteristics are real as in the hyberbolic case, they can be used to solve partial differential equations directly.
Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley   +2 more
openaire   +1 more source

Theory of degenerate second order hyperbolic equations

Siberian Mathematical Journal, 1990
The equation mentioned in the title is: \[ Lu=\nu^ 2(t)u_{tt}- \sum^{n}_{i,j=1}\partial /\partial x_ i(a_{ij}(x,t)u_{x_ j})+au_ t+\sum^{n}_{i=1}b_ iu_{x_ i}+cu=f, \] with \(a_{ij}=a_{ji}\), \(\sum^{n}_{i,j=1}a_{ij}\xi_ i\xi_ j\geq 0\), for any \(\xi \in {\mathbb{R}}^ n\). \(\nu\) (t) is continuous on [0,1] and differentiable on (0,1].
openaire   +2 more sources

Some Remarks on Some Second-order Hyperbolic Differential Equations

Semigroup Forum, 2004
Let \(H\) be a Hilbert space. A function \(u:\mathbb{R}\to H\) is said to be almost automorphic if for every sequence of real numbers \((\sigma_{n})\), there exists a subsequence \((s_{n})\) such that \(g(t)=\lim_{n\to\infty}f(t+s_{n})\) is well defined for each \(t\in \mathbb{R}\), and \(f(t)=\lim_{n\to\infty}g(t-s_{n})\) for each \(t\in \mathbb{R}.\)
openaire   +1 more source

Least-squares Galerkin procedure for second-order hyperbolic equations

Journal of Systems Science and Complexity, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Hui, Rui, Hongxing, Lin, Chao
openaire   +1 more source

Local in Space Energy Estimates for Second-order Hyperbolic Equations

2012
In the first part of the paper we review some recent results concerning the propagation of analytic regularity for the s-Gevrey solutions, with \( s < \overline{m}/(\overline{m}-1) \), to the semilinear (weakly) hyperbolic equations with characteristics of multiplicity \( \leq\overline{m} \).The main results are concerning two special classes of ...
SPAGNOLO, SERGIO, TAGLIALATELA G.
openaire   +2 more sources

Linearization of completely exceptional second order hyperbolic conservative equations

Applicable Analysis, 1995
The formation of nonlinear shocks does not occur for nonlinear hyperbolic partial differential equations which are “completely exceptional”. In some sense the solutions of these equations exhibit a behaviour similar to that of linear equations. We present a procedure which allows to transform, under suitable conditions, such type of equations to linear
DONATO, Andrea Ant, OLIVERI, Francesco
openaire   +1 more source

Second-order equations: hyperbolic equations for functions of two independent variables

1978
We start with the general quasi-linear second-order equation for a function u(x,y): $$ a{u_{xx}} + 2b{u_{xy}} + c{u_{yy}} = d, $$ (1.1) where a,b,c,d depend on x,y,u,u x ,u y . Here the Cauchy problem consists of finding a solution u of (1.1) with given (compatible) values of u,u x ,u y on a curve γ in the xy-plane.
openaire   +1 more source

Finite element approximations with quadrature for second‐order hyperbolic equations

Numerical Methods for Partial Differential Equations, 2002
AbstractIn this article, the effect of numerical quadrature on the finite element Galerkin approximations to the solution of hyperbolic equations has been studied. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived in the L∞(H1), L∞(L2) norms, whereas quasi‐optimal estimate is derived in the L∞(L∞) norm using ...
openaire   +2 more sources

CARLEMAN ESTIMATES AND INVERSE PROBLEMS FOR SECOND ORDER HYPERBOLIC EQUATIONS

Mathematics of the USSR-Sbornik, 1987
The author considers the problem of finding the time-independent coefficients of a second order hyperbolic equation from the Cauchy data at the initial moment and on a part of the lateral surface of a cylindrical domain. Estimates of Hörmander's Carleman type are obtained.
openaire   +2 more sources

Cauchy Problem of the Second-Order Linear Hyperbolic Equations

2017
In order to solve the Cauchy problem of nonlinear wave equations later (see Chap. 7), we will consider in this chapter the following Cauchy problem of n-dimensional linear hyperbolic equations.
Tatsien Li, Yi Zhou
openaire   +1 more source