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Su3liminal
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Homework Statement
Homework Equations
How can I start the proof? Shall I use the Poincare inequality?
The Attempt at a Solution
Well, I know that this norm is defined by
Last edited:
Su3liminal said:Homework Statement
Homework Equations
How can I start the proof? Shall I use the Poincare inequality?
The Attempt at a Solution
Well, I know that this norm is defined by, but still I don't know how to start constructing the proof?
Ray Vickson said:Start by omitting the square root. Take ##\partial / \partial t## inside the integral sign (justify!), then use the DE to eliminate, or at least, modify ##\partial{u^2}/\partial t##.
The L2 norm, also known as the Euclidean norm, is a mathematical concept used to measure the length of a vector in a multi-dimensional space. It is calculated by taking the square root of the sum of squared components of the vector.
Proving that the L2 norm is a non-increasing function of time is important in many fields, such as physics, engineering, and data analysis. It can help in understanding the behavior of systems over time and making predictions about their future states.
The most common way to prove that the L2 norm is a non-increasing function of time is by using mathematical techniques, such as calculus and linear algebra. This involves manipulating the equations that define the L2 norm and showing that it decreases over time.
If the L2 norm is proven to be a non-increasing function of time, it means that the vector being measured is becoming more stable or localized over time. This could indicate a steady state or convergence towards a specific value.
While proving the L2 norm to be a non-increasing function of time is useful in many cases, it may not always be applicable. In some situations, other norms or measures may be more appropriate for capturing the behavior of a system over time.