universal data

Chapter 304
307 chapter

There are two seniors in the second year of research, one is called Zhang Chumen and the other is called Gu Shi.

Both of them can be regarded as direct students of Professor Fang, and they have followed Professor Fang since the undergraduate stage.

Moreover, both of them were directly admitted to graduate school because they had achieved enough achievements at the undergraduate level.

"Teacher, who is this?" Entering the door, Zhang Chumen glanced at Cheng Nuo and asked with a smile.

"Oh, he is Cheng Nuo, who was introduced by Professor Lu. He is about to join our research group. In the next six months, Cheng Nuo will be a member of us. You should take good care of him." Su The professor introduced with a smile.

"Hi senior, I'm Cheng Nuo." Cheng Nuo held out his hand.

"Zhang Chumen."

"Gu Shi."

Senior Gu Shi was very cold, with his arms folded, he just nodded to Cheng Nuo, looking like an outsider.

Senior Zhang Chumen was very enthusiastic and shook hands with Cheng Nuo with a smile.

In terms of age, Zhang Chumen was four or five years older than Cheng Nuo, but he didn't have any shoulders.

He patted his chest, "School Cheng Nuo, don't worry, the teacher has already spoken, and they are all from the same college. If you encounter any problems in the future, just go to the graduate student dormitory and find me."

Cheng Nuo said thank you and accepted the favor.

By chance, Su Xuanqi came out of the kitchen with a plate of dishes.

She put a plate of sweet and sour pork ribs on the coffee table, wiped the sweat from her forehead, put her hips on her hips, and said to the three of Cheng Nuo who were still standing, "What are you guys doing standing here, hurry up and sit down!" Let's go eat."

The three of them hesitated.

Professor Fang sat down the three of them with a smile, "I knew you were coming, so I asked Xiaoqi to cook a few more dishes. I asked you to come over at noon, and you must have not had time to eat. Just right, we Eat and chat."

The three looked at each other and sat down one after another.

After Su Xuanqi brought out all the dishes, she sat on the other side of the sofa with Professor Fang.

A few people chatted while eating, and what they talked about was naturally related to the project.

Zhang Chumen smiled and said, "Teacher, should the name of our project be finalized?"

It was Su Xuanqi who answered, "The teacher told me that the name of this project is "The Monotonicity Method of Bitypical Nonlinear Differential Equations Containing Generalized p-Laplacian Operators"."

"The monotonicity method of bitypical nonlinear differential equations with generalized p-Laplacian operator?" Cheng Nuo whispered.

"Do you feel confused? Haha, to be honest, if I were not a graduate student and heard the name of this topic, I would definitely be confused. But now, I feel like that." Sitting next to Cheng Nuo On the side, Zhang Chumen silently pretended to be cool in front of him, the junior student whom he met for the first time.

Cheng Nuo shrugged, "It's okay."

In fact, after Professor Lu taught the subject, Cheng Nuo went back to learn more about it.

The more he learned about it, the more Cheng Nuo understood why the entire School of Mathematics regarded this research project as so important.

The generalized p-Laplacian operator and the zero point of the maximal operator are indeed hot spots in international research. The field of applied mathematics in Huaguo has also followed this upsurge and carried out many projects. Papers on this aspect are also one after another. articles.

However, to be honest, there are very few topics and papers in Huaguo that can be sold in this area.As for the achievements that can be put on the international stage for the whole world's mathematics peers to learn from, they are even rarer.

Therefore, it is rare for Tsinghua University and Peking University to jointly apply for a topic that represents the most cutting-edge direction of p-Laplacian operators.

Of course, the most cutting-edge issues also mean that there is not much information to refer to.Everything depends on self-exploration.

The burden was heavy, especially for Cheng Nuo, who was still an undergraduate.

Of course, fortunately, there is Professor Fang's thick thigh.

The five chatted while eating.

"Our subject, to put it simply, is to use the perturbation results of the pseudo-monotone operator and the maximum monotone operator's range to obtain a hyperbolic nonlinear differential with a generalized p-Laplacian operator and mixed boundary value conditions. The abstract conclusion that an equation has a unique solution."

"This is an extension of the related research work on nonlinear elliptic equations and parabolic equations with generalized p-Laplacian operators. At the same time, the relationship between the unique solution of the movement and the zero point of a certain maximum monotone operator. Of course, this knowledge is mine Some conjectures, what method will be used in the actual operation process, I can't give a conclusion now." Professor Fang first briefly explained the main research content of the project.

Then, let a few people express their views and talk about their own opinions.

To be honest, among the four, none of them is an expert in this field.

Although the three graduate students are in the field of mathematics, applied mathematics is divided into many research directions. None of the research directions of the three of them is about the p-Laplacian operator, and they have a little bit of knowledge in this area.

Of course, their kind of slightly involved refers to the extent that the full score of the exam is no problem, and it is somewhat difficult to study new content.

Talking about some superficial things, the three of them were very relaxed.

Beginning with Su Xuanqi, the three of them successively expressed their unique insights on this subject, with a lot of formulas and theorems, but none of them specifically talked about more in-depth issues.

When it came to Cheng Nuo at the end, all eyes fell on him.

Cheng Nuo smiled and said slowly, "I don't know as much as my seniors and sisters about this area of ​​expertise, so I'll just talk about the research direction I came up with on this topic. Of course, this is just my guess. I can’t guarantee that it will be implemented.”

"It's okay, you can speak freely, it doesn't matter if you say something wrong." Professor Fang gave Cheng Nuo an encouraging look.

Cheng Nuo coughed lightly and organized his words, "I think our entry point for this topic should be on Banach space!"

Cheng Nuo's tone was filled with inexplicable certainty.

"Banach space? Isn't that part of functional analysis? Does it have something to do with our subject?" The aloof senior Gu Shi frowned and spoke.

"Let Cheng Nuo continue to talk. Mathematics is a subject that connects with each other, and there is no strict division of fields." Professor Fang signaled Cheng Nuo to continue.

Cheng Nuo continued, "Indeed, Banach spaces and maximal monotone operators do not have much correlation, but the project uses some formulas to correlate the two with each other."

“If Ω is a compact Hausdorff space, and let C(Ω) represent the totality of all real (or complex) valued continuous functions on Ω, then C(Ω) becomes a Banach space with respect to the norm. Another example , assuming (Ω, μ) is a positive measure space, let Lp (Ω, μ) represent the totality of all p (p ≥ 1) times summable functions on Ω, then Lp (Ω, μ) becomes a Bana with respect to the norm He Space…”

Cheng Nuo talked eloquently.

A series of formulas blurted out without thinking.

The three of Gu Shi said that they were completely confused.

Professor Fang was the only one who could keep up with Cheng Nuo's train of thought.

Moreover, Professor Fang nodded frequently while listening.

(End of this chapter)