On the Cauchy problem for second order strictly hyperbolic equations with non–regular coefficients

Hirosawa, Fumihiko

doi:10.1002/mana.200310068

Cited by 21 publications

(1 citation statement)

References 8 publications

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“…However, the orientation of mesogens in the photopolymerized LC film has not been studied well. The relationship between the conditions of the alignment layer and the orientation of mesogens in the photopolymerized LC film has not yet been clarified [7,8]. This is critical information for the design of optical compensation films.…”

Section: Introductionmentioning

confidence: 99%

Relationship between Molecular Orientation of Rubbed Polyimide Alignment Layer and That of Liquid-Crystalline Polymer Film Coated on the Alignment Layer

Yamahara

Nakamura

Koide

et al. 2007

Molecular Crystals and Liquid Crystals

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The molecular orientation of the coating type of retardation film was investigated. The retardation film was created by photopolymerization of a liquid-crystalline (LC) monomer coated on a rubbed polyimide alignment layer. The relationship between the molecular orientation of a rubbed polyimide film and that of mesogens in a photopolymerized liquid crystal coated on the polyimide film has been investigated using optical measurements. It was found that the inclination angle of the refractive index ellipsoide and the optical retardation of photopolymerized LC films are strongly related to the optical properties of the rubbed polyimide film regardless of the rubbing conditions.

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Section: Introductionmentioning

confidence: 99%

Relationship between Molecular Orientation of Rubbed Polyimide Alignment Layer and That of Liquid-Crystalline Polymer Film Coated on the Alignment Layer

Yamahara

Nakamura

Koide

et al. 2007

Molecular Crystals and Liquid Crystals

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On second order weakly hyperbolic equations with oscillating coefficients and regularity loss of the solutions

Hirosawa

2010

Mathematische Nachrichten

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Regularity of the solution for the wave equation with constant propagation speed is conserved with respect to time, but such a property is not true in general if the propagation speed is variable with respect to time. The main purpose of this paper is to describe the order of regularity loss of the solution due to the variable coefficient by the following four properties of the coefficient: "smoothness", "oscillations", "degeneration" and "stabilization". Gevrey and C ∞ well-posedness for the wave equations with degenerate coefficients taking into account the interactions of these four properties. Moreover, we prove optimality of these results by constructing some examples.

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Does the loss of regularity really appear?

Reissig

2008

Math Methods in App Sciences

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On the Cauchy problem for second order strictly hyperbolic equations with non–regular coefficients

Cited by 21 publications

References 8 publications

Relationship between Molecular Orientation of Rubbed Polyimide Alignment Layer and That of Liquid-Crystalline Polymer Film Coated on the Alignment Layer

Relationship between Molecular Orientation of Rubbed Polyimide Alignment Layer and That of Liquid-Crystalline Polymer Film Coated on the Alignment Layer

On second order weakly hyperbolic equations with oscillating coefficients and regularity loss of the solutions

Does the loss of regularity really appear?

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