Holomorphic affine and projective connections of hyperbolic type

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.

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A singular boundary value problem for evolution equations of hyperbolic type

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110517 ◽

2021 ◽

Vol 143 ◽

pp. 110517

Author(s):

Anar T. Assanova ◽

Roza E. Uteshova

Keyword(s):

Boundary Value Problem ◽

Evolution Equations ◽

Boundary Value ◽

Hyperbolic Type ◽

Singular Boundary ◽

Singular Boundary Value Problem

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On the Persistence of Lower-Dimensional Tori in Reversible Systems with Hyperbolic-Type Degenerate Equilibrium Point Under Small Perturbations

Acta Applicandae Mathematicae ◽

10.1007/s10440-021-00419-0 ◽

2021 ◽

Vol 173 (1) ◽

Author(s):

Xiaocai Wang ◽

Xiaofei Cao

Keyword(s):

Equilibrium Point ◽

Hyperbolic Type ◽

Reversible Systems ◽

Small Perturbations ◽

Degenerate Equilibrium ◽

Lower Dimensional Tori ◽

Lower Dimensional

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On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory

Russian Journal of Mathematical Physics ◽

10.1134/s106192080601002x ◽

2006 ◽

Vol 13 (1) ◽

pp. 4-12 ◽

Cited By ~ 12

Author(s):

A. I. Aptekarev ◽

Yu. G. Rykov

Keyword(s):

Potential Theory ◽

Hyperbolic Type ◽

Quasilinear Equations ◽

Variational Representation ◽

Representation Of Solutions

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EXISTENCE OF PERIODIC SOLUTIONS FOR A FREE BOUNDARY PROBLEM OF HYPERBOLIC TYPE

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891608001702 ◽

2008 ◽

Vol 05 (04) ◽

pp. 785-806

Author(s):

KAZUAKI NAKANE ◽

TOMOKO SHINOHARA

Keyword(s):

Mathematical Model ◽

Free Boundary ◽

Hyperbolic Equation ◽

Boundary Problem ◽

Free Boundary Problem ◽

Physical Phenomenon ◽

Hyperbolic Type ◽

Existence Of Periodic Solutions ◽

A Free Boundary Problem ◽

Thin Tape

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

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