Results 221 to 230 of about 855 (241)

Local solutions for a nonlinear degenerate Hyperbolic equation

Nonlinear Analysis: Theory, Methods & Applications, 1986
The author investigates local solutions for the initial-boundary value problem associated to the nonlinear degenerated hyperbolic equation of the type \(u_{tt}-M(\int_{\Omega}| \nabla u|^ 2dx)\Delta u=0,\) which comes from the mathematical description of the vibrations of an elastic stretched string.
Ebihara, Y., Medeiros, L. A., Milla Miranda, M.   +2 more
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Weakly Degenerate Hyperbolic Equations

Differential Equations, 2003
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A nonlocal problem for degenerate hyperbolic equation

Russian Mathematics, 2017
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Repin, O. A., Kumykova, S. K.
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Maslov’s canonical operator for degenerate hyperbolic equations

Russian Journal of Mathematical Physics, 2014
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A degenerate hyperbolic equation under Levi conditions

ANNALI DELL'UNIVERSITA' DI FERRARA, 2006
In the present study the author deals with the second-order equations of the form \[ \Biggl(D^2_t- \sum^n_{i,j=1} a_{ij}(t, x)D_{x_i} D_{x_j}+ \sum^n_{j=1} b_j(t, x)D_{x_j}+ C(t, x)\Biggr) u(t, x)= 0,\tag{1} \] where \(t\in [0,T]\), \(x\in\mathbb{R}^n\), \(D= {1\over i}\partial\), with \[ a(t,x,\xi):= \sum^n_{i,j=1} a_{ij}(t, x)\xi_i\xi_j\geq 0,\quad t\
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Möbius transformation and degenerate hyperbolic equation

Advances in Applied Clifford Algebras, 2001
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Hyperbolic phenomena in a strongly degenerate parabolic equation

Archive for Rational Mechanics and Analysis, 1992
The authors consider the problem \(u_ t=(\varphi(u)\psi(u_ x))_ x\) for \(x\in\mathbb{R}\), \(t>0\), \(u(x,0)=u_ 0(x)\) for \(x\in\mathbb{R}\) where \(\varphi:\mathbb{R}\to\mathbb{R}^ +\) is smooth and strictly positive, and \(\psi:\mathbb{R}\to\mathbb{R}\) is a smooth, odd function such that \(\psi'>0\) in \(\mathbb{R}\) and \(\lim_{s\to\infty}\psi(s)\
BERTSCH, MICHIEL, Dal Passo, R.
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Degenerated nonlinear hyperbolic equation with discontinuous coefficients

Proceedings of the Indian Academy of Sciences - Section A, 1985
The author considers a general nonlinear hyperbolic equation in the region \(Q:=D\times [0,T]\) where D is a bounded domain in \({\mathbb{R}}^ n\) with smooth boundary \(\Gamma\). It is assumed that D is partitioned by a hypersurface \(\Gamma_ 1\) into regions \(D_ 1\) and \(D_ 2\) and the notation \(\gamma =\Gamma_ 1\times [0,T]\), \(S=\Gamma \times ...
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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].
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Smooth Local Solutions to Degenerate Hyperbolic Monge-Ampère Equations

Annals of PDE, 2019
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