Looking at a solitary initial state

In summary, the conversation is about investigating the deformation of a solitary initial state represented by the equation u0(x) = a0x2(1-x)2 as time goes on. It is mentioned that the deformation will not occur if c is constant. The speaker also asks for suggestions on which methods to use for this task. However, more context is needed, such as the location of the differential equation and the initial problem, as well as the definition of c.
  • #1
simo1
29
0
I have this equation

u0(x) = a0x2(1-x)2 for 0≤ x ≤ 1
= 0 for x>1
i have to investigate how will a solitary initial state such as the one above deform as time goes on.

I know it will not deform if c is constant. when they say I must do this by a well-lnown method and produce video frmaes, could you suggest which methods to use
 
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  • #2
We need a lot more context to help you out, I think.

1. Where is the differential equation? All I see here is a function definition.

2. In what context does this differential equation arise? Can you give us the initial problem?

3. What is $c$?
 

FAQ: Looking at a solitary initial state

What is a solitary initial state?

A solitary initial state refers to a state in which a system or object exists alone, without any external influences or interactions. It is a starting point from which the system can evolve or change over time.

Why is looking at a solitary initial state important in scientific research?

Studying solitary initial states allows scientists to observe the natural behavior or properties of a system without any external influences. This can help in understanding the fundamental principles and mechanisms underlying a system, and can also serve as a baseline for comparison in more complex scenarios.

Can a solitary initial state exist in nature?

Yes, solitary initial states can exist in nature. Examples include the formation of isolated planets or stars in space, the initial stages of embryonic development in single-celled organisms, and the study of isolated particles in particle physics.

How is a solitary initial state different from an equilibrium state?

A solitary initial state and an equilibrium state are different in that a solitary initial state is a starting point with no external influences, while an equilibrium state is a stable state where the system's internal and external forces are balanced. A solitary initial state can evolve into an equilibrium state over time.

What are some techniques used to study a solitary initial state?

Scientists may use various techniques such as mathematical modeling, computer simulations, and experimental observations to study solitary initial states. These techniques allow for the observation and analysis of the system's behavior without any external influences.

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