Could anyone introduce me to the Bratu problem?

[hanson]

Hi all.
Can someone tell me what a bratu problem is?
I have just an equation on hand but I have no clue in what this equation is describing and how it is derived. Could anyone here refer me to some texts or websites about the bratu problem?

 

[HallsofIvy]

I had never heard of the "Bratu problem" but I goodled on it and immediately got these:
http://www.nada.kth.se/kurser/kth/2D1290/comp03_3.pdf
http://www.uz.ac.zw/science/maths/samsa/journal/volumes/2003/01/brtu.pdf

Is this the "Bratu" you mean:
http://bratu.oltenia.ro/

 

[mehrnazz]

hi
i am a math student and right now i am working on Bratu;s problem if u search Bratu;s problem in google and sciencedirect u can find a lot of articles about that. Bratu type equation is u''(x) + a*e^u(x)=0

 

[mehrnazz]

Bratu’s problem appears in combustion theory of fuel ignition. combustion
is rapid chemical reaction of two or more substances with a characteristic
liberation of heat and light. The burning of a fuel (e.g., wood, coal, oil, or
natural gas) in air is a familiar example of combustion. also bratu’s problem
has application in the Chandrasekhar model of the expansion of the universe
and nanotechnology.

 

[CellCoree]

The Bratu problem is a mathematical problem that involves finding the solution to a specific nonlinear boundary value problem. It is named after the Romanian mathematician Gheorghe Bratu who first proposed it in 1933. The problem has applications in various fields such as fluid mechanics, heat transfer, and population dynamics.

The equation you have on hand is likely the Bratu equation, which is a second-order nonlinear differential equation. Its solution represents the steady-state temperature distribution in a heated plate with a constant heat source. The equation can be solved analytically in some special cases, but in general, numerical methods are used to find a solution.

If you are interested in learning more about the Bratu problem, I recommend checking out some textbooks on nonlinear boundary value problems or searching for articles and papers on the topic. Some good starting points could be "Nonlinear Boundary Value Problems" by J. L. Massera and J. J. Schäffer or "Numerical Solution of Nonlinear Boundary Value Problems with Applications" by R. P. Agarwal and D. O'Regan.

You can also find some online resources such as lecture notes or research papers that discuss the Bratu problem in more detail. I hope this helps introduce you to the Bratu problem and provides some resources for further study.