Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Ervin, V. J."'
Autor:
Ervin, V. J.
In this paper we analyze the existence, uniqueness and regularity of the solution to the generalized, variable diffusivity, fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$. For $\alpha$ the order of the differential operator, our res
Externí odkaz:
http://arxiv.org/abs/2405.02457
Autor:
Ervin, V. J.
In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$, we establish a characterization of the weighted Sobolev space $H_{\beta}^{s}(\Omega)$ in terms of the decay rate of Fourier-Jacobi coeff
Externí odkaz:
http://arxiv.org/abs/2404.04658
In this article we show that the fractional Laplacian in $R^{2}$ can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. Using this factored form we introduce a generalization of the fractiona
Externí odkaz:
http://arxiv.org/abs/2304.12419
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion operator may lose coercivity due to the variable coefficient, which m
Externí odkaz:
http://arxiv.org/abs/2203.11705
Autor:
Bentley, Alistair, Ervin, V. J.
In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a two dimens
Externí odkaz:
http://arxiv.org/abs/2004.10720
In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution to this equation was obtained. Using the explicit form of the boundar
Externí odkaz:
http://arxiv.org/abs/2002.02330
Autor:
Ervin, V. J.
In this report we investigate the regularity of the solution to the fractional diffusion, advection, reaction equation on a bounded domain in $\mathbb{R}^{1}$. The analysis is performed in the weighted Sobolev spaces, $H_{(a , b)}^{s}(\mathrm{I})$. T
Externí odkaz:
http://arxiv.org/abs/1911.03261
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient fractional dif
Externí odkaz:
http://arxiv.org/abs/1902.10208
In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral operator. Under a suitable transformation the variable coefficient equation
Externí odkaz:
http://arxiv.org/abs/1811.00582
In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower order, cons
Externí odkaz:
http://arxiv.org/abs/1810.12420