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feynman1
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how to show or prove that the shape of the solution of a heat equation can only go smoother and smoother but not the opposite as time increases?
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Sorry, my Google search of your term coarsened seems to say the opposite of smoother. Could you please expand on your question, and post links to relevant articles?feynman1 said:how to show or prove that the solution of a heat equation can only go coarsened/smoother as time increases?
graduate school / PhD level is the right category.berkeman said:Sorry, my Google search of your term coarsened seems to say the opposite of smoother. Could you please expand on your question, and post links to relevant articles?
And your marked your thread start with an "A" prefix, which means you want the discussion to be at the graduate school / PhD level. Is that really what you intended?
feynman1 said:maybe coarsen means differently in different fields, so let's forget about coarsen
https://www.merriam-webster.com/dictionary/coarsenDefinition of coarsen
transitive verb
: to make coarse
intransitive verb
: to become coarse
Please post links to your reading about your question. Thank you.feynman1 said:how to show or prove that the solution of a heat equation can only go coarsened/smoother as time increases?
sorry but if there was such a link there'd be explanations then I wouldn't have posted here. It's just about time irreversibility of heat equations.berkeman said:Please post links to your reading about your question. Thank you.
So you're really going to make us Google search that phrase? Please do that search and tell us what you don't understand. Seriously.feynman1 said:time irreversibility of heat equations
A heat equation is a mathematical model that describes how heat is distributed in a given region over time.
Yes, the solution of a heat equation is known to become smoother as time increases. This is because as time passes, heat is gradually distributed and diffused throughout the region, resulting in a more uniform temperature distribution.
The solution of a heat equation is affected by various factors such as the initial temperature distribution, the material properties of the region, and the boundary conditions.
No, the solution of a heat equation may not always be a smooth function. It depends on the initial conditions and boundary conditions of the region. In some cases, the solution may have discontinuities or sharp changes.
The heat equation is used in various fields such as physics, engineering, and economics to model and understand heat transfer processes. It is commonly used in designing and optimizing heating and cooling systems, predicting temperature changes in materials, and analyzing heat flow in different scenarios.