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The generalized Benjamin-Bona-Mahony equation in R n with singular initial data
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TLDR
In this article, the authors consider the equation U t -ΔU t -div(Ψ(u))=0 avec t ≥ 0, x ∈ Ω ou Ω=R n and on specialise au cas ou chaque Φ j est un polynome de degre γ ou moins.Abstract:
On considere l'equation U t -ΔU t -div(Ψ(u))=0 avec t≥0, x∈Ω ou Ω=R n et on specialise au cas ou chaque Φ j est un polynome de degre γ ou moins. On etablit l'existence et l'unicite des solutions globales fortesread more
Citations
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Random attractors for the stochastic Benjamin–Bona–Mahony equation on unbounded domains
TL;DR: The existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony equation defined on an unbounded domain was proved in this article, which is invariant and attracts every pulled-back tempered random set under the forward flow.
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Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R 3
TL;DR: In this article, the authors study the asymptotic behavior of the solutions of the Benjamin-Bona-Mahony equation defined on R 3, and provide a sufficient condition to verify the compactness of an evolution equation defined in an unbounded domain.
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Existence and convergence of solutions for the generalized BBM-Burgers equations with dissipative term
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Decay of solutions of generalized Benjamin-Bona-Mahony equations
TL;DR: In this article, a discussion of global solutions to the initial value problems for generalized Banjamin-Bona-Mahony equations is presented with the initial data in some certain Sobolev spaces.
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Long time dynamics for a damped Benjamin–Bona–Mahony equation in low regularity spaces
TL;DR: In this article, the authors proved the existence of a global attractor in L 2 if the force belongs to L 2 and showed that the global attractors has finite fractal dimension in the sharp regularity space H 2.
References
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Model Equations for Long Waves in Nonlinear Dispersive Systems
TL;DR: In this article, the authors studied mathematical models for the unidirectional propagation of long waves in systems that manifest nonlinear and dispersive effects of a particular but common kind.
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Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system
TL;DR: In this paper, a local regular solution for the Navier-Stokes system was constructed for a class of semilinear parabolic equations with dimensionless or scaling invariant norm, where p and q are chosen so that the norm of Lq(0, T; Lp) is dimensionless.
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Solutions in Lr of the Navier-Stokes initial value problem
Yoshikazu Giga,Tetsuro Miyakawa +1 more
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Semilinear evolution equations in Banach spaces
TL;DR: In this paper, the authors studied the evolution equation u′(t) = Au(t + J(u(t)), t ⩾ 0, where etA is a C 0 semi-group on a Banach space E, and J is a singular non-linear mapping defined on a subset of E. Under certain integrability conditions on the Kt, they proved existence and uniqueness of local solutions to the integral equation u(t), = etA φ + ∝0t Kt − s(u (s)) ds for all φ
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