Results 221 to 230 of about 718 (256)

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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Certain nonlocal problem for a degenerate hyperbolic equation

Mathematical Notes, 1992
The equation \((*)\) \(| y|^ m u_{xx}- u_{yy}=0\), \(m>0\) is considered in a domain bounded by characteristics of \((*)\). Values of integrals of \(u\) along characteristics are given. The author proves uniqueness and existence of the solution to the problem mentioned above.
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On a variational inequality for a degenerate quasilinear hyperbolic equation

Applied Mathematics and Computation, 2003
The author studies a unilateral problem for the nonhomogeneous degenerate Kirchhoff equation with a blowing up term. Using the penalty method and Galerkin's approximation, existence and uniqueness results are obtained.
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Boundary problems for a class of degenerate hyperbolic equations

Siberian Mathematical Journal, 1984
The author considers the equation \(xu_{xx}-yu_{yy}+(\alpha -m)u_ x- (\beta -n)u_ y=0\), provided ...
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Energy estimates for a class of degenerate hyperbolic equations

Mathematische Annalen, 2009
Considered is the Cauchy problem for a linear degenerate inhomogeneous hyperbolic equation in one dimension. The leading coefficient which is allowed to vanish is decomposed in \(a(x ,t)= q(x ,t)K(x ,t)\), where \(K(x ,t)\), is a nonnegative smooth function and \(q(x ,t)\) is a positive smooth function. In case all coefficients are smooth functions on \
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Continuous Observability of Hyperbolic Equations under Degenerate Sensors

2017
In this chapter we intend to extend our studies of the observability properties of partial differential equations to a large class of linear second-order partial differential equations (PDEs) of hyperbolic type in n spatial dimensions. We will show that both the L ∞ (0, T; R n+1)- and C([0, T[; R n+1)-continuous observability properties are possible ...
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