Applications and time‐domain solution of higher‐order parabolic equations in underwater acoustics

Michael D. Collins

doi:10.1121/1.398101

Applications and time‐domain solution of higher‐order parabolic equations in underwater acoustics

The Journal of the Acoustical Society of America ◽

10.1121/1.398101 ◽

1989 ◽

Vol 86 (3) ◽

pp. 1097-1102 ◽

Cited By ~ 81

Author(s):

Michael D. Collins

Keyword(s):

Time Domain ◽

Parabolic Equations ◽

Underwater Acoustics ◽

Higher Order ◽

Higher Order Parabolic Equations

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On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-009-0025-x ◽

2009 ◽

Vol 16 (5) ◽

pp. 597-655 ◽

Cited By ~ 12

Author(s):

V. A. Galaktionov

Keyword(s):

Parabolic Equations ◽

Boundary Point ◽

Blow Up ◽

Higher Order ◽

Type Criterion ◽

Higher Order Parabolic Equations

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Existence results for doubly nonlinear higher order parabolic equations on unbounded domains

Mathematische Annalen ◽

10.1007/bf01456275 ◽

1988 ◽

Vol 279 (3) ◽

pp. 373-394 ◽

Cited By ~ 60

Author(s):

F. Bernis

Keyword(s):

Parabolic Equations ◽

Unbounded Domains ◽

Higher Order ◽

Existence Results ◽

Doubly Nonlinear ◽

Higher Order Parabolic Equations

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Energy‐conserving and reciprocal solutions for higher‐order parabolic equations

The Journal of the Acoustical Society of America ◽

10.1121/1.426454 ◽

1999 ◽

Vol 105 (2) ◽

pp. 1362-1363 ◽

Cited By ~ 1

Author(s):

Dmitry Yu. Mikhin

Keyword(s):

Parabolic Equations ◽

Higher Order ◽

Energy Conserving ◽

Higher Order Parabolic Equations

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Phase space path integral on torus for the fundamental solution of higher-order parabolic equations

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-020-00341-3 ◽

2020 ◽

Vol 11 (3) ◽

pp. 1059-1083

Author(s):

Naoto Kumano-go ◽

Keiya Uchida

Keyword(s):

Phase Space ◽

Fundamental Solution ◽

Path Integral ◽

Parabolic Equations ◽

Higher Order ◽

Higher Order Parabolic Equations

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Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity

Interfaces and Free Boundaries ◽

10.4171/ifb/40 ◽

2001 ◽

pp. 233-264 ◽

Cited By ~ 26

Author(s):

Daniele Andreucci ◽

Anatoli Tedeev

Keyword(s):

Thin Film ◽

Parabolic Equations ◽

Higher Order ◽

Finite Speed Of Propagation ◽

Finite Speed ◽

Thin Film Equation ◽

Speed Of Propagation ◽

Higher Order Parabolic Equations ◽

General Nonlinearity

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On nonexistence of Baras–Goldstein type for higher-order parabolic equations with singular potentials

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-10-04855-5 ◽

2010 ◽

Vol 362 (08) ◽

pp. 4117-4136 ◽

Cited By ~ 10

Author(s):

V. A. Galaktionov ◽

I. V. Kamotski

Keyword(s):

Parabolic Equations ◽

Higher Order ◽

Singular Potentials ◽

Higher Order Parabolic Equations

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Boundary value problems for higher order parabolic equations

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-00-02702-1 ◽

2000 ◽

Vol 353 (2) ◽

pp. 809-838 ◽

Cited By ~ 1

Author(s):

Russell M. Brown ◽

Wei Hu

Keyword(s):

Boundary Value Problems ◽

Parabolic Equations ◽

Boundary Value ◽

Higher Order ◽

Higher Order Parabolic Equations

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Benchmark calculations for higher‐order parabolic equations

The Journal of the Acoustical Society of America ◽

10.1121/1.399453 ◽

1990 ◽

Vol 87 (4) ◽

pp. 1535-1538 ◽

Cited By ~ 36

Author(s):

Michael D. Collins

Keyword(s):

Parabolic Equations ◽

Higher Order ◽

Higher Order Parabolic Equations

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Split‐step/finite‐difference and split‐step/Lanczos algorithms for solving alternative higher‐order parabolic equations

The Journal of the Acoustical Society of America ◽

10.1121/1.410490 ◽

1994 ◽

Vol 96 (1) ◽

pp. 396-405 ◽

Cited By ~ 9

Author(s):

David Yevick ◽

David J. Thomson

Keyword(s):

Finite Difference ◽

Parabolic Equations ◽

Higher Order ◽

Higher Order Parabolic Equations

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Multipoint problem for higher-order parabolic equations in a parallelepiped

Nonlinear Oscillations ◽

10.1007/s11072-010-0081-5 ◽

2009 ◽

Vol 12 (3) ◽

pp. 346-357

Author(s):

B. I. Ptashnyk ◽

I. R. Tymkiv

Keyword(s):

Parabolic Equations ◽

Higher Order ◽

Multipoint Problem ◽

Higher Order Parabolic Equations

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