Results 231 to 240 of about 36,044 (276)

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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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
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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
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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
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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.
Fritz John
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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
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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 ...
O. O. Pokutnyi
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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
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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
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J.I. Ramos
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Second- and Third-Order Noncentered Difference Schemes for Nonlinear Hyperbolic Equations

, 1973
R. F. Warming, P. Kutler, H. Lomax
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