Sentence examples for established decay from inspiring English sources

Under suitable growth conditions on, he also established decay results for weak and strong solutions.

Al-Gharabli and Messaoudi [6] studied the following nonlinear plate problem: textstylebegin{cases} { u_{tt} + Delta^{2} u + u + h u_{t}) = kuln |u| u,} & mbox{in } Omegatimes 0,+infty), { u=frac{partial u}{partialeta}=0,} &mbox{on } partial Omegatimes[0,+infty), { u x,0)=u_{0}(x), qquad u_{t} x,0)=u_{1}(x),} &mbox{in } Omega, end{cases} (1.1) and established decay of solutions.

Caries was assessed as defined by the International Caries Detection and Assessment System (ICDAS) Code 3 as established decay [ 42].

A total of 49.6% of the children were caries free, 8.3% had early stage decay, 14% had untreated established decay and 28.1% had untreated severe decay.

Obvious decay experience included caries at the pulpal (severe decay) and visual dentinal (established decay) levels as well as at the enamel level to improve recording of the disease threshold.

We establish decay rates of the energy by considering ideas from the work of Messaoudi [15].

The aim of this section is to establish decay estimates of the solution operators to (1.1).

The aim of this subsection is to establish decay estimates of the solution operators G ( t ) and H ( t ) appearing in (2.9) and (2.10), respectively.

The aim of this section is to establish decay estimates of the solution operators G ( t ) and H ( t ) appearing in the solution formula (2.10).

Therefore the significant role of MC has been addressed in a wide range of field experiments and approaches to establish decay models.

There are several long standing problems on the incompressible Navier Stokes flows in 2D exterior domains, which claim how to characterize L1-summability of the 2D N-S flows; whether the total net force exerted on the boundary is finite; and how to establish decay results of higher-order spatial derivatives, including the weighted cases.