Remarks on the asymptotic behaviour of the solution to parabolic problems in domains becoming unbounded

Chipot, Michel; Rougirel, Arnaud

doi:10.1016/s0362-546x(01)00151-1

Cited by 11 publications

(14 citation statements)

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“…types of elliptic, parabolic and hyperbolic problems involving different boundary conditions, for instance see [4], [5], [6], [7], [8], [13], [14]. Our aim of this paper is to investigate the asymptotic behavior of the solution to the Dirichlet problem for the fractional Laplace operator.…”

Section: Mathematics Subject Classification 2010: 35b40 35r09mentioning

confidence: 99%

On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity

Chowdhury

Roy

2016

Commun. Contemp. Math.

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The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic problems by Chipot and Rougirel in [3], where the force functions are considered on the cross section of domains, we prove the non-local counterpart of their result.Furthermore, recently in [15] Yeressian established a weighted estimate for solutions of nonlocal Dirichlet problems which exhibit the asymptotic behavior. The case when s = 1/2 was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this article, we extend this result to each order between 0 and 1.

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Section: Mathematics Subject Classification 2010: 35b40 35r09mentioning

confidence: 99%

On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity

Chowdhury

Roy

2016

Commun. Contemp. Math.

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“…Theorem 1.4. Under the assumption (1), (8) and q = 2, if u and u ∞ satisfy (3) and (5) respectively then one has…”

Section: (Communicated By José a Carrillo)mentioning

confidence: 99%

“…For q > 2, affine functions are the only functions which satisfies (8) and hence cannot satisfy (1) simultaneously. This justifies the condition (8).…”

Section: (Communicated By José a Carrillo)mentioning

confidence: 99%

On some variational problems set on domains tending to infinity

Chipot¹,

Mojsic²,

Roy³

2016

DCDS-A

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“…The case of the sequence of the k-th eigenfunction is considered in Theorem 3.8. This kind of issue, namely the approximation of the solutions of problems set on cylinders by the solution of problems set on their section, is addressed in [2], [3], [4], [5], [6], [7], [8] for some differential equations, variational inequalities or systems. If one wants to normalize u k in such a way that its L 2 -norm is equal to one, one is led to choose A k such that Suppose now that we want to find the eigenvalues and eigenfunctions of the problem…”

Section: Introductionmentioning

confidence: 99%

On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded

Chipot¹,

Rougirel²

2008

Trans. Amer. Math. Soc.

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Abstract. The aim of this work is to analyze the asymptotic behaviour of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions. In particular, in the case of a linear elliptic operator in divergence form, we prove that the sequence of the k-th eigenvalues convergences to the first eigenvalue of an elliptic problems set on the section of the domain. Moreover, an optimal rate of convergence of this sequence is given.

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Remarks on the asymptotic behaviour of the solution to parabolic problems in domains becoming unbounded

Cited by 11 publications

References 0 publications

On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity

On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity

On some variational problems set on domains tending to infinity

On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded

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