Ein singulär gestörtes Problem für eine lineare parabolische Differentialgleichung beliebiger Ordnung
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Hans-Görg Roos (1978)
Commentationes Mathematicae Universitatis Carolinae
Coclite, Giuseppe Maria, Coclite, Mario Michele (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
J. J. H. Miller, S. Wang (1990)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
James M. Greenberg (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also present some...
James M. Greenberg (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also present...
Carlos E. Kenig, Fanghua Lin, Zhongwei Shen (2013)
Journal of the European Mathematical Society
For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an estimate in for solutions with Dirichlet condition.
Peter Constantin, Komla Domelevo, Jean-Michel Roquejoffre, Lenya Ryzhik (2006)
Journal of the European Mathematical Society
A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.
Eva Rovderová (1992)
Mathematica Bohemica
In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).
Kamel Al-Khaled (2014)
Applications of Mathematics
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
Alves, Claudianor Oliveira, Carrião, Paulo C., Faria, Luiz F.O. (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Tian, Qiaoyu, Huang, Shuibo (2009)
The Journal of Nonlinear Sciences and its Applications
de Groen, P.P.N., Karadzhov, G.E. (1998)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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