Results 231 to 240 of about 8,120 (265)
Some of the next articles are maybe not open access.
On a Spatial Problem of Darboux Type for a Second-Order Hyperbolic Equation
gmj, 1995Abstract The theorem of unique solvability of a spatial problem of Darboux type in Sobolev space is proved for a second-order hyperbolic equation.
openaire +2 more sources
Local in Space Energy Estimates for Second-order Hyperbolic Equations
2012In 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
CARLEMAN ESTIMATES AND INVERSE PROBLEMS FOR SECOND ORDER HYPERBOLIC EQUATIONS
Mathematics of the USSR-Sbornik, 1987The 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
Periodic solutions of second-order hyperbolic integrodifferential equations
Ukrainian Mathematical Journal, 1987The author is concerned with the existence and uniqueness of solutions to the problem \[ u_{tt}-u_{xx}=\epsilon f(x,t,u,u_ t,u_ x)+\epsilon \int^{h(x,t)}_{0}\phi (x,t,s,u(x,s),u_ t(x,s),u_ x(x,s))ds, \] u(0,t)\(=u(\pi,t)=0\), where \(\epsilon\) is a parameter, \(h: \{\) \(0\leq x\leq \pi\), \(t\in R\}\to R\), while f(x,t,u,v,w) and \(\phi\) (x,t,s,u,v ...
Khoma, G. P., Gromyak, M. I.
openaire +2 more sources
Some Remarks on Some Second-order Hyperbolic Differential Equations
Semigroup Forum, 2004Let \(H\) 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
Finite element approximations with quadrature for second‐order hyperbolic equations
Numerical Methods for Partial Differential Equations, 2002AbstractIn 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
Nonlocal Problem for Fourth-Order Loaded Hyperbolic Equations
Russian Mathematics, 2023A T Assanova, Assanova A T
exaly
Singularities of solutions for nonlinear hyperbolic equations of second order
2000We 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”.
openaire +1 more source
The problem of cauchy for linear, hyperbolic equations of second order
Communications on Pure and Applied Mathematics, 1954openaire +2 more sources
On second order weakly hyperbolic equations and the Gevrey classes
2000The authors study the weakly hyperbolic Cauchy problem \[ \partial^2_t u-\sum^n_{k,l=1} a_{kl}(t) \partial^2_{x_k x_l}u+ b(t) u=0,\qquad u(0,x)= u_0(x),\quad \partial_t u(0, x)= u_1(x). \] Here weakly hyperbolic means that \(\sum^n_{k,l=1} a_{k_l}(t) \xi_k\xi_l\geq 0\). It is a delicate problem to prove well-posedness results.
COLOMBINI, FERRUCCIO, T. NISHITANI
openaire +3 more sources