Solitary waves of generalized Kadomtsev–Petviashvili equations

Bouard, Anne de; Saut, Jean‐Claude

doi:10.1016/s0294-1449(97)80145-x

Cited by 159 publications

(236 citation statements)

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“…) is a solution of the problem (3,4). Then for all λ > 0, there exists A > 0 and Q a 1-valuated polynomial with positive coefficients, so that for all t ∈ [0, T ),…”

Section: Nonlinear Resultsmentioning

confidence: 99%

“…We also give a local existence theorem whatever the velocity of the shear and the initial data are: (3) and (4) …”

Section: Theorem 22 There Existsmentioning

confidence: 99%

“…• we found a sequence of solutions of approximated PDE's of (3,4). These solutions are denoted by (v n , h n );…”

Section: Proof Of the Global Existencementioning

confidence: 99%

“…The last term is the one treated previously and showing the result on the first one is dealing with 4 . By integrating by parts with respect to x, one has I = −3I 5 −2I 6 , where 6 .…”

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confidence: 97%

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Mathematical analysis of the stabilization of lamellar phases by a shear stress

Torri

2002

ESAIM: COCV

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Abstract. We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette−Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments.Mathematics Subject Classification. 35B35, 35Q35, 76E05, 76U05.

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“…) is a solution of the problem (3,4). Then for all λ > 0, there exists A > 0 and Q a 1-valuated polynomial with positive coefficients, so that for all t ∈ [0, T ),…”

Section: Nonlinear Resultsmentioning

confidence: 99%

“…We also give a local existence theorem whatever the velocity of the shear and the initial data are: (3) and (4) …”

Section: Theorem 22 There Existsmentioning

confidence: 99%

“…• we found a sequence of solutions of approximated PDE's of (3,4). These solutions are denoted by (v n , h n );…”

Section: Proof Of the Global Existencementioning

confidence: 99%

“…The last term is the one treated previously and showing the result on the first one is dealing with 4 . By integrating by parts with respect to x, one has I = −3I 5 −2I 6 , where 6 .…”

mentioning

confidence: 97%

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