The phrase "assumption of solution" is not commonly used in written English and may be unclear without context.
It could be used in discussions related to problem-solving or theoretical frameworks where a solution is presumed to be valid.
Example: "The assumption of solution in this case allows us to simplify the analysis and focus on the key variables."
Alternatives: "presumed solution" or "hypothetical solution".
One is that discontinuous control systems are non-smooth, which violates the fundamental assumptions of solution theories and the applicability of Lyapunov's stability theory is questionable.
The convergence analysis of iterative finite element approximation to the solution was done under an assumption of 'small' solution or source data which guarantees the uniqueness of the nonlinear coupled system.
The building blocks are one-bump solutions at the mountain pass level and the existence of such solutions as well as multi-bump solutions is guaranteed by a nondegeneracy assumption of the solutions near the mountain pass level.
In this case, based on the coercivity assumption, the existence of solution for the generalized vector equilibrium problem are deeply discussed, see [1 13].
By the assumption on uniqueness of solution, we have v x, t) = E c (x, t) and the entire sequence {u k } converges to E c as k → ��.
Based on the coercivity assumption, the existence of solution for (vector) equilibrium problem received much attention of researchers, see e.g., [1 8].
It is shown that the application of perturbation method imposes some limitations on the order of magnitudes of the terms in the differential equation of the motion; as a result out of the domain where the ordering assumption of the perturbation solution does not hold, some periodic solutions as well as some vital bifurcation points are missed.
The assumption of a harmonic solution for the uncoupled equations led to wave equations.
It considers the convection, migration and diffusion mechanisms under the assumption of a dilute solution, mass conservation, and local electro-neutrality.
The role of the charge density σ on Δ is quite asymmetrical on both sides of Eσ = 0: (i) for σ < 0 a very small Δ variation agrees with a model of weak metal solvent interaction; (ii) for σ > 0, large Δ variations, strongly depending on the crystal orientation, must be interpreted through the assumption of strong metal-solution interaction.
