Results 41 to 49 of about 191 (49)

Fractional diffusion equation with the distributed order Caputo derivative [PDF]

arXiv, 2017
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only integrable.
arxiv  

Invariant measures for systems of Kolmogorov equations [PDF]

arXiv, 2017
In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these measures are absolutely continuous with respect to the Lebesgue measure and study some of their main properties. Finally,
arxiv  

Approximate Cloaking for The Heat Equation via Transformation Optics [PDF]

arXiv, 2018
In this paper, we establish approximate cloaking for the heat equation via transformation optics. We show that the degree of visibility is of the order $\epsilon$ in three dimensions and $|\ln\epsilon|^{-1}$ in two dimensions, where $\epsilon$ is the regularization parameter.
arxiv  

On the Cauchy problem for the reaction-diffusion system with point-interaction in $\mathbb R^2$ [PDF]

arXiv
The paper studies the existence of solutions for the reaction-diffusion equation in $\mathbb R^2$ with point-interaction laplacian $\Delta_\alpha$ with $\alpha\in(-\infty,+\infty]$, assuming the functions to remain on the absolute continuous projection space.
arxiv  

Ricci flow on surfaces with conical singularities, II [PDF]

arXiv, 2013
In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2\pi$. In this case, convergence results are obtained if the Euler number is nonpositive.
arxiv  

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

Open Mathematics, 2013
Bárta Tomáš
doaj   +1 more source

Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: I. Existence [PDF]

arXiv
We consider evolution (non-stationary) space-periodic solutions to the $n$-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition.
arxiv  

Regularity results for elliptic and parabolic systems of partial differential equations [PDF]

arXiv
We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over $\R^d$. Consequently, we deduce relevant regularity results both in H\"
arxiv  

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Towards Microscopic and Nonlocal Models of Tumour Invasion of Tissue

, 2008
M. Lachowicz
semanticscholar   +1 more source