Sentence examples for behavior for the solution from inspiring English sources

In this paper, we consider the limit behavior for the solution of the Cauchy problem of the energy-critical complex Ginzburg Landau equation in Rn, n⩾3.

Comparisons results and asymptotic behavior for the solution for particular choices of the heat source, initial, and boundary data are also obtained.

A heat conduction problem of the type (1.1) to (1.4) for a semi-infinite material was analyzed in [5, 6], where results on existence, uniqueness and asymptotic behavior for the solution were obtained.

In our article, we are going to study the large time asymptotic behavior for the solution of (1.1) and (1.2) by comparing it to the Barenblatt-type solution, let us give some details.

In other frameworks, a class of heat conduction problems characterized by a uniform heat source given as a multivalued function from ℝ into itself was studied in [3] with results regarding existence, uniqueness and asymptotic behavior for the solution.

Combining Theorem 2.1 with Theorem V.3.7 in [31] we can establish the following property of asymptotic behavior for the solution semigroup associated to the homogeneous problem (2.5 - 2.6 2.5 - 2.6

In this section, we consider the nonexistence of complicated asymptotic behavior for the solutions of Problem (1.1 - 1.2 1.1 - 1.2 initial value (u_{0}in withsigma}(matheb{R}^{N})).

The complexity of asymptotic behavior for the solutions is considered for (sigma=frac{p}{q-p+1}) in Section 4 and for (frac{p}{q-p+1}

end{aligned} (4.1) Now we give the result that for (sigma=frac{p}{q-p+1}), the complicated asymptotic behavior for the solutions of Problem (1.1 - 1.2 1.1 - 1.2 initial value (u_{0}in withigma}^(matheb {R}^{N})) can happen.

Inspired by the above papers, in this paper, we try to find out how the initial value belonging to (W_{sigma}(mathbb{R}^{N})) with different σ affects the complicated asymptotic behavior for the solutions of Problem (1.1 - 1.2 1.1 - 1.2mbda=1).

In fact, we find that if (0behavior for the solutions of Problem (1.1 - 1.2 1.1 - 1.2 initial value (u_{0}in withigma}^(matheb{R}^{N})) cannot happen.