Solutions for Some Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 1
Round 1
Reviewer 1 Report
In the article, the author has presented seven techniques for obtaining and characterizing weak solutions to mathematical physics equations. The methods were developed within a comprehensive framework and are supported by detailed proofs and numerous auxiliary propositions. The author aims to facilitate the application of these techniques to real-world problems that arise in the modeling of physical phenomena. The importance of these operators and their potential relevance in modeling a significant class of real-world phenomena motivated the author to present and thoroughly detail seven procedures. These procedures are accompanied by numerous applications and a general overview of their application in specialized domains. The utilization of specific variational methods simplifies the complete problem solution through the application of appropriate numerical and computational algorithms. The presentation of the theoretical results, along with detailed demonstrations, provides a complete development of the topic. This presentation is intended to serve as a comprehensive resource for those seeking a deeper understanding of these procedures. .
Upon reading this paper, I discovered that the results presented are both innovative and captivating. However, I noticed that the paper reads more like an extensive review article or book chapter, with 75 references cited. Consequently, I recommend that the author revise the paper to concentrate more heavily on the new method introduced, while delving deeper into the detailed explanations of the more established findings. This will help to streamline the paper and ensure that the focus remains on the novel approach being presented.
This paper need to be rewritten
Author Response
Dear reviewer,
Thank you for the careful reading and positive appreciation of my manuscript. A detailed answer can be found attached.
Kind regards,
Irina Meghea
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Collecting this work is hard and time consuming on Solutions for some mathematical physics problems issued from modeling real phenomena
* Most of part of this paper is very well written. But there is less new research in the paper. It is written like lecture notes.
* This paper is sometimes review article or sometimes research article.
* If it is review paper, then reduce the proofs of existing results.
* If it is research article, then reduce the review results from existing literature.
*Many things have been written as preliminaries which are not part of present research.
*Many definitions and results are given without citations.
*Many proofs are repeated works from other existing literature.
*Mostly things are written from self-cited papers.
*Many results are similar and repeated proofs.
*Conclusion is very long. It should reduce.
*Mostly references are old except few self-citations.
Rest of corrections can be seen in attached pdf in yellow color.
This paper needs major improvements.
Comments for author File: Comments.pdf
It is ok except few typo errors.
Author Response
A detailed answer is attached below.
Author Response File: Author Response.pdf
Reviewer 3 Report
The article "Solutions of some problems of mathematical physics arising from the simulation of real phenomena" is devoted to the theoretical aspects of studying the equations of mathematical physics, which contain p-Laplacian and p-pseudo-Laplacian. Weak solutions of the Dirichlet and Neumann problems are studied using various approaches. The author has done a great job, the article is a review on the chosen topic. However, the article contains the following methodological flaws:
1. The numbering of propositions, corollaries, remarks, and also theorems should be double numbered, for example, as references in formulas. The article is too long and difficult to navigate.
2. All indices, parameters, designations must have the same form. Either an oblique outline or a straight line. Pay attention to the subscripts, they must be really low. Likewise superscripts. You have to check and read. The same applies to the text, for example, line 1320. Somewhere the fonts are different.
3. The author gives surnames in parentheses. Apparently, these are the authors of works in which this or that problem was considered. It is necessary to give a link to the source, so the reader quickly understands what is at stake.
4. In the work, I did not see the solutions themselves in the framework of modeling real phenomena, as well as their graphs. There are only assertions that such solutions exist. It would be nice for the author to think about practical applications of the results obtained in the article.
5. There are typos in the article, for example, line 11 instead of Newmann needs Neumann, there are extra brackets in some places. You need to read the article.
The language needs a little checking
Author Response
A detailed answer is attached below.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The current version can be accepted
Reviewer 2 Report
The author has included all my comments and suggestions. We recommend this paper for possible publication in Axioms.
Reviewer 3 Report
The author corrected my comments, so the article can be recommended for publication.
