scholarly journals Precise propagation of singularities for a hyperbolic system with characteristics of variable multiplicity

1986 ◽  
Vol 101 ◽  
pp. 111-130 ◽  
Author(s):  
Chisato Iwasaki ◽  
Yoshinori Morimoto
Keyword(s):  
Cauchy Problem ◽  
Wave Front ◽  
Hyperbolic System ◽  
Wave Front Set ◽  
Variable Multiplicity ◽  
The Cauchy Problem ◽  
Propagation Of Singularities ◽  
Admissible Trajectory

In this paper we consider the Cauchy problem for a hyperbolic system with characteristics of variable multiplicity and construct a certain solution whose wave front set propagates precisely along the so-called “broken null bicharacteristic flow”, in other words, along the admissible trajectory if we use the terminology of [6].

scholarly journals Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials

2015 ◽  
Vol 27 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Elena Cordero ◽  
Fabio Nicola ◽  
Luigi Rodino
Keyword(s):  
Wave Front ◽  
Modulation Spaces ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Front Set ◽  
Local Propagation ◽  
The Cauchy Problem ◽  
Wave Front Sets ◽  
Propagation Of Singularities ◽  
Gabor Wave Front Set

We consider Schrödinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may not even be differentiable. The well-posedness of the Cauchy problem is proved in the frame of the modulation spaces, and results of micro-local propagation of singularities are given in terms of Gabor wave front sets.

scholarly journals Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zenggui Wang
Keyword(s):  
Cauchy Problem ◽  
Life Span ◽  
Hyperbolic System ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Classical Solutions ◽  
Quasilinear Hyperbolic System ◽  
Inverse Mean Curvature Flow ◽  
The Cauchy Problem

In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system in terms of Riemann invariants. By the theory on the local solution for the Cauchy problem of the quasilinear hyperbolic system, we discuss life-span of classical solutions to the Cauchy problem of hyperbolic inverse mean curvature.

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