1,927 research outputs found
Critical Thresholds in 2D Restricted Euler-Poisson Equations
We provide a complete description of the critical threshold phenomena for the
two-dimensional localized Euler-Poisson equations, introduced by the authors in
[Liu & Tadmor, Comm. Math Phys., To appear]. Here, the questions of global
regularity vs. finite-time breakdown for the 2D Restricted Euler-Poisson
solutions are classified in terms of precise explicit formulae, describing a
remarkable variety of critical threshold surfaces of initial configurations. In
particular, it is shown that the 2D critical thresholds depend on the relative
size of three quantities: the initial density, the initial divergence as well
as the initial spectral gap, that is, the difference between the two
eigenvalues of the initial velocity gradient
Optimal financing and dividend distribution in a general diffusion model with regime switching
We study the optimal financing and dividend distribution problem with
restricted dividend rates in a diffusion type surplus model where the drift and
volatility coefficients are general functions of the level of surplus and the
external environment regime. The environment regime is modeled by a Markov
process. Both capital injections and dividend payments incur expenses. The
objective is to maximize the expectation of the total discounted dividends
minus the total cost of capital injections. We prove that it is optimal to
inject capitals only when the surplus tends to fall below zero and to pay out
dividends at the maximal rate when the surplus is at or above the threshold
dependent on the environment regime
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