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pro vyhledávání: '"Cuesta, Carlota M."'
In this paper, we develop an iterative method, based on the Bartels-Stewart algorithm to solve $N$-dimensional matrix equations, that relies on the Schur decomposition of the matrices involved. We remark that, unlike other possible implementations of
Externí odkaz:
http://arxiv.org/abs/2412.15840
In this paper, we develop a fast and accurate pseudospectral method to approximate numerically the half Laplacian $(-\Delta)^{1/2}$ of a function on $\mathbb{R}$, which is equivalent to the Hilbert transform of the derivative of the function. The mai
Externí odkaz:
http://arxiv.org/abs/2306.05009
Autor:
Cuesta, Carlota M., Diez, Xuban
We study the large time behaviour of the solutions of a non-local regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order $1+\alpha$, with $\alpha\in(0,1)$, which is a Riesz-Feller operator. The n
Externí odkaz:
http://arxiv.org/abs/2302.03981
In this article, we develop a new method to approximate numerically the fractional Laplacian of functions defined on $\mathbb R$, as well as some more general singular integrals. After mapping $\mathbb R$ into a finite interval, we discretize the int
Externí odkaz:
http://arxiv.org/abs/2212.05143
In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the ${}_2F_1$ Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the Higgins functions, the Christov functions, and their sine-
Externí odkaz:
http://arxiv.org/abs/2001.08825
Autor:
Cuesta, Carlota M., Diez, Xuban
We study a nonlocal regularisation of a scalar conservation law given by a fractional derivative of order between one and two. The nonlocal operator is of Riesz-Feller type with skewness two minus its order. This equation describes the internal struc
Externí odkaz:
http://arxiv.org/abs/1909.00685
In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over $\mathbb R$, we map the unbounded domai
Externí odkaz:
http://arxiv.org/abs/1908.09143
We study self-similar solutions of the thin-film equation, with mobility exponent m in (0,4], that describe the lifting of an isolated touch-down point given by an initial profile of the form |x|. This provides a mechanism for non-uniqueness of the t
Externí odkaz:
http://arxiv.org/abs/1708.00243
Autor:
Cuesta, Carlota M., Achleitner, Franz
We add a theorem to [J. Differential Equations 257 (2014), no. 3, 720--758] by F. Achleitner, C.M. Cuesta and S. Hittmeir. In that paper we studied travelling wave solutions of a Korteweg-de Vries-Burgers type equation with a non-local diffusion term
Externí odkaz:
http://arxiv.org/abs/1604.05931
We consider a two-dimensional model of a porous medium where circular grains are uniformly distributed in a squared container. We assume that such medium is partially filled with water and that the stationary interface separating the water phase from
Externí odkaz:
http://arxiv.org/abs/1505.03676