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1. CMB 2011 (vol 55 pp. 623)
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The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations In this paper, we consider the Cauchy problem
$$
\begin{cases}
u_{t}=\Delta(u^{m}), &x\in{}\mathbb{R}^{N}, t>0, N\geq3,
\\
% ^^----- here
u(x,0)=u_{0}(x), &x\in{}\mathbb{R}^{N}.
\end{cases}
$$
We will prove that:
(i) for
$m_{c} Keywords:fast diffusion equations, Cauchy problem, continuous dependence on nonlinearity Categories:35K05, 35K10, 35K15 |
2. CMB 1999 (vol 42 pp. 169)
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Heat Kernels of Lorentz Cones We obtain an explicit formula for heat kernels of Lorentz cones, a
family of classical symmetric cones. By this formula, the heat
kernel of a Lorentz cone is expressed by a function of time $t$ and
two eigenvalues of an element in the cone. We obtain also upper and
lower bounds for the heat kernels of Lorentz cones.
Keywords:Lorentz cone, symmetric cone, Jordan algebra, heat kernel, heat equation, Laplace-Beltrami operator, eigenvalues Categories:35K05, 43A85, 35K15, 80A20 |