Sentence examples for by considering the solution from inspiring English sources
By considering the solution u k of the regularized problem (1.10) and using Moser's iteration technique, we get u k 's local bounded properties and the local bounded properties of the L p -norm of the gradient ∇ u k.
So the blow-up time of v cannot be larger than that of u. u blows up at finite time T, by considering the solution at time (T-varepsilon) as initial data, we may assume that the blow-up time is as small as desired.
Similarly, Figures 2, 3 are plotted respectively by taking (mathtt{k}=2) and 3. Figures 4, 5, 6 are plotted by considering the solution given in (35) by taking (nu =0.5, 0.7, 0.9, 1, 1.5) and (mathtt{k}=1,2,3).
By considering the solution of a single ellipsoïdal inhomogeneity in the homogenization problem it is possible to observe the significant influence of the geometry, shape and spatial distribution of inhomogeneities on the effective thermal conductivity and its dependence with the saturation degree of liquid phase.
The model is developed based on the basic heat transfer equation, and by considering the solution's and the coolant's convective heat transfer coefficient (h) under the forced flow condition.
The usefulness was assessed by considering the solutions based on the number of people in each class (hereby rejecting solutions with small groups: minimum N = 200).
The validation of the solution is verified by considering the static solution of the beam and comparing the degraded solution to a well-known result.
Firstly, we can easily obtain the quantum correction by only considering the solution of the ground state of the quantum system since it is independent of the number of nodes of the wave function for exactly solvable quantum system.
Simply supported beams are analyzed first by considering the fundamental solution of an infinite beam, and second as a case of a narrow plate with simply supported and roller boundary conditions.
The heteroplasmy h = m2/(m1 + m2) is straightforwardly addressable by considering the above solutions for m1 and m2.
It is clear that both the approaches are close to one another but the modified methodology is efficient and requires less computations than earlier technique in terms of considering the solution preferences by the decision maker at each level.
