Asymptotic behaviour of a thermosyphon model with binary fluids

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

Download Full-text

Well-posedness and asymptotic behaviour of a wave equation with non-monotone memory kernel

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01525-7 ◽

2021 ◽

Vol 72 (2) ◽

Author(s):

Rongsheng Mu ◽

Genqi Xu

Keyword(s):

Wave Equation ◽

Asymptotic Behaviour ◽

Well Posedness ◽

Memory Kernel

Download Full-text

Asymptotic behaviour of ground state solutions for the fractional Hénon equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125456 ◽

2021 ◽

pp. 125456

Author(s):

Haixia Chen ◽

Xiaolin Xu ◽

Xiaolong Yang

Keyword(s):

Asymptotic Behaviour ◽

Ground State ◽

Ground State Solutions ◽

Hénon Equation

Download Full-text

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500015341 ◽

1981 ◽

Vol 90 (1-2) ◽

pp. 63-70 ◽

Cited By ~ 5

Author(s):

Bernd Carl

Keyword(s):

Banach Space ◽

Asymptotic Behaviour ◽

Besov Spaces ◽

Eigenvalue Problems ◽

Function Spaces ◽

Sequence Spaces ◽

Entropy Numbers ◽

Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Download Full-text