Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles

Round 1

Reviewer 1 Report

 

Authors study reaction-diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The paper is well written and very interesting. All formulas are correct.  I recommend accepting the paper after theses corrections.   

 

 

 

1.       Please check the English in you paper. For example, in the abstract and keywords, please correct the following

a.       In the abstract: Replace “By means of 4 generalized Fatou’s Lemma we prove” by “By means of  generalized Fatou’s Lemma, we prove“

b.      In the abstract: Remove “Bibliography: 53 titles.” From the abstract.

c.       In the keyword: Replace “trajectory attractors”  by “Trajectory attractors”

d.      These just example, so please review the English in the whole paper carefully.

2. Please can you write more details how you prove inequality (23).

3. Please prove proposition 5.

4. Please can you explain the prove of theorem 2 in more details.

5. Write conclusion section.

6. Most of the references are old references and the number of references is large. You can remove some of them.

7. It will be better to the paper if you can add at least one example to show the power of your main theorem.

Author Response

The answer to the reviewers.

 

We want to express our thanks to the anonymous reviewers for a careful reading of the work and valuable comments that allowed us to improve the presentation of the results.

 

We have improved the language of presentation and have corrected typos and inaccuracies.

 

We improved the proof of inequality (23). We added the proofs of Proposition 4, 5 and Theorem 2. Moreover, we added Proposition 10 for more convenience.

 

We added an example to illustrate and better understand the results.

 

We added the conclusions.

 

We removed several old references in the bibliography reducing the number of references.

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

The answer to the reviewers.

 

We want to express our thanks to the anonymous reviewers for a careful reading of the work and valuable comments that allowed us to improve the presentation of the results.

 

We have improved the language of presentation and have corrected typos and inaccuracies.

 

We improved the proof of inequality (23). We added the proofs of Proposition 4, 5 and Theorem 2. Moreover, we added Proposition 10 for more convenience.

 

We added an example to illustrate and better understand the results.

 

We added the conclusions.

 

We removed several old references in the bibliography reducing the number of references.