As the flame expands, the local minima of the initial perturbation determine the primary troughs which have a dominant effect on the long term evolution since they constrain the waveangle over which secondary cells can form and interact and define the periodicity of the problem.
It has been found, however, that the convergence of the iterative solvers for linear equations slows down when the solutions show anomalies related to the periodicity of the problems.
In the following section we will study the existence, uniqueness and periodicity of solutions of problem (7) and in Section 3 we will apply these results to the case of problems with reflection.
In the remaining of this section, we will consider the almost periodicity and pseudo almost periodicity of the bounded weak solution of problem (4.1) under the assumption that f and h have the corresponding properties.
To show the pseudo almost periodicity of a weak solution u of problem (4.1), the process consists of two parts: obtaining its almost periodic component and then the ergodic perturbation.
The problem concerning periodicity of semicycles of difference equations was solved in very general settings by Berg and Stević in [9], partially motivated also by [10].
Many papers on max-type difference equations and systems deal with the problem of periodicity of their solutions (see, for example, [1, 3, 4, 7, 12, 13, 16, 17], and the references therein), while global attractivity results can be found, for example, in [2, 5, 10, 14].
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period.
Due to the periodicity, the problem can be reduced to that in a unit cell.
This can be classified as a periodicity identification problem.
