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Source-type solutions and asymptotic behaviour for a diffusion-convection equation

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The article was published on 1991-08-01 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Asymptotic analysis & Method of matched asymptotic expansions.

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Asymptotic behavior for the vorticity equations in dimensions two and three

TL;DR: Asymptotic behavior for the vorticity equations in dimensions two and three has been studied in this paper, where the authors consider the case where the equations are expressed as partial differential equations.
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On the blow-up of solutions of a convective reaction diffusion equation

TL;DR: In this paper, the authors studied the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equation, where u is a scalar function of the spatial variable x ∈ N and time t > 0, a ∈ ℝV, a ≠ 0, 1 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time.
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Asymptotics of solutions of nonlinear parabolic equations

TL;DR: In this paper, the large time behavior of solutions to the Cauchy problem of the following nonlinear parabolic equations was studied under the optimal growth conditions on the smooth nonlinear function F(u,Dxu, Dx2u), and the global existence results were obtained.
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Convergence of moderately interacting particle systems to a diffusion–convection equation

TL;DR: In this article, the authors give a probabilistic interpretation of the solution of a diffusion-convection equation and obtain the solution as the propagation of chaos limit of a sequence of moderately interacting particle systems.
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