We are interested in the well‐posedness and exponential decay of Moore–Gibson–Thompson equation with memory τtttu+αttu+ht(0)Au+bAtu∫0∞ht′(s)Au(ts)ds=0.$$ tau {partial}_{tt t}u+alpha {partial}_{tt}u+{h}_t(0)mathcal{A}u+bmathcal{A}{...
Bi-exponential fitting of theoretical results versus the effective coupling to the plasmonic structure. (a) The superradiance and subradience decay times\({\tau }_{1}\)and\({\tau }_{2}\)normalized by the decay time without metamaterial\({\tau }_{0}\). Dashed lines show average of\({...
For the imaginary part, we then get the equation: $$\begin{aligned} \sin ({\text {Im}}(y)) = 2\ell +\frac{2\tan ^{-1}(1/\theta )}{\pi } \quad \text {for some}\, \ell \in \mathbb {Z}\end{aligned}$$ which is not possible for \(\left| {\text {Im}}(y)\right...
Equation (8) can be presented in a more compact form after scaling the variables as s = c/|1 − A|, \(z=x\surd |1-A|\) and τ = t |1 − A|, which gives $${s}_{\tau }={s}_{zz}-{s}^{2}\pm s\beta erfc(z/2\sqrt{\tau })$$ (9) with...
. This function also gives us the asymptotic behavior of the solution of TF equation at infinity. The solution of the TF equation has been effectively approximated using variational approaches based on a combination of exponential functions. Although an approximate solution having exponential decay will...
Write an equation to model the situation. An exponential function f has a 3-unit growth factor of 1.61. What is the 1-unit growth factor for f? The function P(t) = 1.5e^{0.3t} represents exponential growth or decay. a. What is the initial quantity? ...
which leads to the following equation for estimating τ0after the substitution of parameters (32): $${{M}_{2}}\tau _{0}^{2} = 2\ln \left( {\frac{{5{{M}_{2}}}{{{B}^{2}}}{{M}_{2}}\tau _{0}^{2}} \right) + \ln \left( {1 - \frac{{{B}^{2}}}{{5{{M}...
exponential decay exponential distribution exponential equation exponential expression exponential function exponential horn Exponential Moving Average Exponential quantity exponential return exponential series exponentially exponentiation exponible export export credit ...
weak particle decay/ exponential decay lawshort decay timestau decay into tau neutrino+Xquantum mechanicsmassive particleshidden variablesupper limitlower limit/ A1335 Decays of leptons A1460J Heavy leptons A0365B Foundations, theory of quantum measurement, miscellaneous quantum theories...
energy decayviscoelastic wave equationPOSITIVE-INITIAL-ENERGYBLOW-UPSOURCE TERMSEVOLUTION-EQUATIONSGLOBAL NONEXISTENCECAUCHY-PROBLEMEXISTENCEIn this paper we consider the nonlinear viscoelastic equation u(tt) - Delta + integral(t)(0) g(t-tau)Delta u(tau)d tau + u(t) = vertical bar u vertical ...