35B40 ChineseLibraryClassifications:O175-29 KeyW0rds:Globalexistence;exponentialdecay;nonlinearviscoelasticequation. 1 Introduction Inthispaperweinvestigatetheglobalexistenceanduniformdecayrateofenergyof solutionsforthenonlinearviscoelasticproblemwithdamping: “leut,-△“一△“ +/0g(f—T)△“(T)dT+l“l一2...
Furthermore, by using Gronwall estimates, exponential decay of the solution is also proved under some smallness assumptions on the parameters appearing in the system and on the initial data. Finally some examples are illustrated.doi:10.1002/mma.7936Alessandro Paolucci...
ExponentialGrowthandDecay指数增长和衰变
35L90,35B40ChineseLibraryClassifications:O175-29KeyW0rds:Globalexistence;exponentialdecay;nonlinearviscoelasticequation.1IntroductionInthispaperweinvestigatetheglobalexistenceanduniformdecayrateofenergyofsolutionsforthenonlinearviscoelasticproblemwithdamping:“leut,-△“一△“+/0g(f—T)△“(T)dT+l“l一2“=...
Exponential functions can also be applied in real world contexts to determine things like population growth and radioactive decay. In these cases, the function will not be like above (f(x) = bx) but rather the formula must account for other factors. For example, in the case of radioactive...
chapter. The relatively brief description belies the importance of this function in characterizing the behavior of various physical processes. In particular, exponentials are solutions to equations describing processes where the rate of growth or decay of a quantityxis proportional to the amount ofx...
6(b), the distance distribu- tions have similar rates of exponential decay indicating that the model parameter s has little influence on the exponential tails of distributions when fixing the parameter l of the density function. In conclusion, the result of proof agrees with the simulations very...
Exponential: X ~ Exp(m) where m = the decay parameterpdf: f(x) = me−mxe−mx where x≥ 0 and m > 0cdf: P(X≤ x) = 1 –e−mxe−mxmean μ=1mμ=1mstandard deviation σ = µpercentile, k: k = ln(AreaToTheLeftOfK)−mln(AreaToTheLeftOfK)−m...
exponential decay Learning Style To achieve what is expected of you . . . allocate sufficient study time briefly revise the prerequisite material attempt every guided exercise and most of the other exercises 1. Exponents revisited We have seen in Chapter 1 (Block 2) the meaning to be ...
As t increases, the elements of etA may grow before they decay. If λ and ? are both negative and α is fairly large, the graph in Figure 1 is typical. Several algorithms make direct or indirect use of the identity esA = (esA/m )m . The di?culty occurs when s/m is under the ...