The Cauchy problem for a tenth-order thin film equation I.  Bifurcation of oscillatory fundamental solutions

Pablo Álvarez-Caudevilla; Jonathan D. Evans; Victor A. Galaktionov

doi:10.1007/s00009-013-0263-3

The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions

Pablo Álvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov

Department of Mathematical Sciences

Universidad Carlos III de Madrid

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

Abstract

Fundamental global similarity solutions of the tenth-order thin film equation
u_t=∇.(|u|ⁿ∇Δ⁴u) in R^N ×₊, where n > 0 are studied. The main approach consists in passing to the limit n→0⁺ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation
u_t =Δ⁵u_t in R^N ×R₊.

Original language	English
Pages (from-to)	1761-1792
Journal	Mediterranean Journal of Mathematics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s00009-013-0263-3
Publication status	Published - Nov 2013

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title = "The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions",

abstract = "Fundamental global similarity solutions of the tenth-order thin film equation ut=∇.(|u|n∇Δ4u) in RN ×+, where n > 0 are studied. The main approach consists in passing to the limit n→0+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation ut =Δ5ut in RN ×R+ .",

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AU - Álvarez-Caudevilla, Pablo

AU - Evans, Jonathan D.

AU - Galaktionov, Victor A.

PY - 2013/11

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AB - Fundamental global similarity solutions of the tenth-order thin film equation ut=∇.(|u|n∇Δ4u) in RN ×+, where n > 0 are studied. The main approach consists in passing to the limit n→0+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation ut =Δ5ut in RN ×R+ .

UR - https://www.scopus.com/pages/publications/84886641349

UR - http://dx.doi.org/10.1007/s00009-013-0263-3

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EP - 1792

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

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The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions

Abstract

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