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Next, by this method we obtain the regularity in time of the solution.
In Section 3 we present the results on the unique existence and the regularity in time of the generalized solution.
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As an application we analyse the quasi sure regularity in time of the stochastic flow of diffeomorphisms generated by a stochastic differential equation with smooth coefficients.
We also investigate continuous and compact embeddings of W and regularity in time of the solution.
We find that their traffic is distinguishable by 1) the regularity in the release time of client commands, 2) the trend and magnitude of traffic burstiness in multiple time scales, and 3) the sensitivity to different network conditions.
To the best knowledge of the authors of this paper, this is the first time to consider the regularity in the category of the Lorentz spaces with variable exponents for the weak solution of variational inequalities (1.1) under minimal regular assumptions on the leading coefficients and the boundary of domain.
Using Ragnarok Onlineas a case study, they have shown that the traffic corresponding to bots and human players is distinguishable in various respects, such as the regularity in client response times, the trend and magnitude of traffic burstiness in multiple time scales, and user sensitivity to network conditions.
The regularity in the spatial variable can then be converted into regularity in time.
In rodents several reflexes and behavioral responses show a remarkable regularity in their time of appearance and subsequent maturation, thus representing a reliable tool for assessing abnormalities in early neurodevelopment [ 27, 28].
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}
We prove the propagation of regularity, uniformly in time, for the scaled solutions of the one-dimensional dissipative Maxwell models introduced in [D.
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