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Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant
This paper is concerned with the asymptotic behavior of the solution to the
Euler equations with time-depending damping on quadrant , \begin{equation}\notag \partial_t v
-
\partial_x u=0, \qquad \partial_t u
+
\partial_x p(v)
=\displaystyle
-\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary
condition or null-Neumann boundary condition on . We show that the
corresponding initial-boundary value problem admits a unique global smooth
solution which tends time-asymptotically to the nonlinear diffusion wave.
Compared with the previous work about Euler equations with constant coefficient
damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156,
439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918),
we obtain a general result when the initial perturbation belongs to the same
space. In addition, our main novelty lies in the facts that the cut-off points
of the convergence rates are different from our previous result about the
Cauchy problem. Our proof is based on the classical energy method and the
analyses of the nonlinear diffusion wave
Exciton Binding Energy of Monolayer WS2
The optical properties of monolayer transition metal dichalcogenides (TMDC)
feature prominent excitonic natures. Here we report an experimental approach
toward measuring the exciton binding energy of monolayer WS2 with linear
differential transmission spectroscopy and two-photon photoluminescence
excitation spectroscopy (TP-PLE). TP-PLE measurements show the exciton binding
energy of 0.71eV around K valley in the Brillouin zone. The trion binding
energy of 34meV, two-photon absorption cross section 4X10^{4}cm^{2}W^{-2}S^{-1}
at 780nm and exciton-exciton annihilation rate around 0.5cm^{2}/s are
experimentally obtained.Comment: 5page,3 figure
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