Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4469
Abstract: In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity: utt+Δ2θu+2μ(−Δ)θut+|ut|p−1ut=0,t≥0,x∈Rn, with μ>0, θ is a positive integer, and p>1+4θ/n, in space dimension n∈(2θ,4θ). We… read more here.
Keywords: self similar; equation critical; similar asymptotic; asymptotic profile ... See more keywords
Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3581-3
Abstract: In this paper, a $$(3+1)$$(3+1)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six bilinear equations and involves nine… read more here.
Keywords: nonlinear evolution; wave solutions; transformation; dimensional nonlinear ... See more keywords
Dynamics of lump collision phenomena to the (3+1)-dimensional nonlinear evolution equation
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2021.104347
Abstract: Abstract The lump solutions have been shown to be one of the most effective solutions for nonlinear evolution problems. The resilient Hirota bilinear method is used to evaluate the integrable (3+1)-dimensional nonlinear evolution equation in… read more here.
Keywords: dimensional nonlinear; evolution equation; nonlinear evolution; evolution ... See more keywords
A constitutive model for thixotropic cemented tailings backfill pastes
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Non-newtonian Fluid Mechanics"
DOI: 10.1016/j.jnnfm.2021.104548
Abstract: Abstract The thixotropic properties of fresh cemented tailing backfill (CTB) pastes applied in underground backfilling are investigated. Reversibility of thixotropy, equilibrium rheology, and stress decay curves of CTB pastes are discussed. A constitutive model that… read more here.
Keywords: evolution equation; thixotropic; constitutive model; model ... See more keywords
A kinematic evolution equation for the dynamic contact angle and some consequences
Sign Up to like & getrecommendations! Published in 2019 at "Physica D: Nonlinear Phenomena"
DOI: 10.1016/j.physd.2019.01.008
Abstract: Abstract We investigate the moving contact line problem for two-phase incompressible flows with a kinematic approach. The key idea is to derive an evolution equation for the contact angle in terms of the transporting velocity… read more here.
Keywords: contact angle; contact; evolution equation;
Asymptotic behaviour of a nonautonomous evolution equation governed by a quasi-nonexpansive operator
Sign Up to like & getrecommendations! Published in 2021 at "Optimization"
DOI: 10.1080/02331934.2021.1949314
Abstract: We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the… read more here.
Keywords: governed quasi; nonautonomous evolution; equation governed; evolution equation ... See more keywords
Evolution equation for multi-photon states in turbulence
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab3db9
Abstract: The recently developed Wigner functional theory is used to formulate an evolution equation for arbitrary multi-photon states, propagating through a turbulent atmosphere under arbitrary conditions. The resulting evolution equation, which is obtained from an infinitesimal… read more here.
Keywords: multi photon; equation multi; photon states; evolution equation ... See more keywords
Blow-up of Solutions of the Cauchy Problem for a Nonlinear Schrödinger Evolution Equation
Sign Up to like & getrecommendations! Published in 2018 at "Doklady Mathematics"
DOI: 10.1134/s1064562418070165
Abstract: The solution of the Cauchy problem for a nonlinear Schrödinger evolution equation with certain initial data is proved to blow up in a finite time, which is estimated from above. Additionally, lower bounds for the… read more here.
Keywords: nonlinear schr; cauchy problem; dinger evolution; problem nonlinear ... See more keywords
Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
Sign Up to like & getrecommendations! Published in 2018 at "Georgian Mathematical Journal"
DOI: 10.1515/gmj-2018-0004
Abstract: Abstract In the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator represents the sum of positive definite self-adjoint operators. The fourth-order accuracy decomposition… read more here.
Keywords: decomposition scheme; scheme; order accuracy; evolution equation ... See more keywords
Fifth order evolution equation of gravity-capillary waves
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DOI: 10.21914/anziamj.v59i0.10867
Abstract: We extend the evolution equation for weak nonlinear gravity–capillary waves by including fifth-order nonlinear terms. Stability properties of a uniform Stokes gravity–capillary wave train is studied using the evolution equation obtained here. The region of… read more here.
Keywords: gravity capillary; order; evolution; evolution equation ... See more keywords