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We consider a class of SKT type reaction-cross diffusion models with vanishing random diffusion coefficients. For homogeneous Dirichlet boundary conditions we prove non-existence of global-in-time non-trivial non-negative smooth... more
We consider a class of SKT type reaction-cross diffusion models with vanishing random diffusion coefficients. For homogeneous Dirichlet boundary conditions we prove non-existence of global-in-time non-trivial non-negative smooth solutions. Some numerical results are also presented, suggesting the possibility of finite-time extinction.
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In this paper, we give one intrinsic inequality for spacelike hypersurfaces in de Sitter space and a sufficient and necessary condition for such hypersurfaces to be totally geodesic.
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Research Interests:
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The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the... more
The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the exterior area $(r>2GM)$ to the interior one $(r<2GM)$. As a contrast to its maximally extension in the Kruskal coordinates, we provide a comoving coordinate system from the view of the observers freely falling into the black hole in the radial direction. We find an interesting fact that the spatial part in this coordinate system is maximally symmetric $(E_3)$, i.e., along the world lines of these observers, the Schwarzschild black hole can be decomposed into a family of maximally symmetric subspaces.