Motivated by these results we investigate the existence and regularity of time-dependent global attractors for a class of nonclassical reaction-diffusion equations textstylebegin{cases} u_{t}- varepsilon(t triangle u_{t}- triangle u+lambda u=f u)+ g(x), & xinOmega, u|_{partialOmega}=0, & tin mathbb{R}, u x,tau)=u_{tau}(x), & tgeqtau.
Based on the notation of time-dependent attractors, we prove the existence and the regularity of time-dependent global attractors for a class of nonclassical reaction-diffusion equations when the forcing term (g(x in H^{-1}(Omega)) and the nonlinear function satisfies the critical exponent growth, which is weaker than the conditions used in (Jing and Liu in Appl. Anal. 94 7):1439-1449, 2015).
In order to obtain the compactness properties of (n_{varepsilon}), (w_{varepsilon}) and (c_{varepsilon}), we need to derive some regularity properties of time derivatives.
There's no room for error; every part of a Soundgarden song is exposed, in arrangements that cantilever slow-moving lines — from Mr. Thayil's guitar, which sometimes hints at Indian raga modes, and from Mr. Cornell's aching voice, rising way up without losing its rasp — over double-time salvos from bass and drums, usually evading the regularity of 4/4 time.
Complexity Sample entropy as a measure of pattern complexity or degree of regularity of the time series.
Roughly speaking, the compatibility condition (3) is equivalent to the (L^{2} -integrability of (sqrt{rho}u_{t}) at (t=0), which is naturaL^{2} -integrabilityl rofe in deducing the regularity of the time derivativesqrt{rho}u_{t}
Low values of entropy imply predictability and high regularity of a time series data.
By avoiding the framework of Gevrey-functions, whish is typically used for the time-varying case, it is shown that the backstepping method can be employed without severe limitations on the regularity of the time-varying terms.
Storing this information in the knowledge base of each vessel may have great contribution to the design of OMDTN. Figure 7e, f illustrates the periodic regularity of contact times.
In this paper, following the general lines of the approach used in [2 4], we investigate the existence and regularity of the time-dependent attractors for the process (U t,tau)) generated by (1.1) under weaker conditions than [1].
