Some results on the boundedness, uniqueness, and continuous dependence on initial data of solutions are established under some suitable conditions.
Using this we study almost everywhere convergence to initial data of solutions of the wave equation associated to the Hermite operator.
In this paper, some new finite difference inequalities in two independent variables are established, which can be used as a handy tool in the study of boundedness, uniqueness, continuous dependence on initial data of solutions of certain difference equations.
We will illustrate the usefulness of the established results by applying them to study the boundedness, uniqueness, and continuous dependence on initial data of solutions of certain difference equations.
Finite difference inequalities in one or two independent variables which provide explicit bounds play a fundamental role in the study of boundedness, uniqueness, and continuous dependence on initial data of solutions of difference equations.
In this study, we prove the existence, uniqueness convergence of the weak generalized solution, continuous dependent upon the data of the solution; and we construct an iteration algorithm for the numerical solution of this problem.
Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, convergence of the weak generalized solution, and also continuous dependence upon the data of the solution are shown by using the generalized Fourier method.
With the experimental data of K2SO4 solution a considerable improvement in the variance of the finally estimated concentration was obtained.
The absorbance data of this solution were recorded (at 380 to 780 nm) after each addition, against a reagent blank.
Under some natural regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown.
