**[An update made on 2 January 2013 appears near the end]**

The following is the question I raised today at the Mathematics Stack Exchange [^]. (It is only today that I became a member there.)

**The Question:**

Assume the simplest linear diffusion equation: , where is the temperature and is the thermal diffusivity.

The domain is finite, say, . (If the assumption of an infinite domain makes it possible (or more convenient) to answer this question, then please assume so. However, the question of interest primarily pertains to a finite domain.)

Assume that the initial temperature profile has a compact support, say over .

After the passage of an arbitrarily small but finite duration of time:

(i) would the temperature profile necessarily have support everywhere over the entire domain?

(ii) or, is it possible that a solution may still have some compact support over some finite interval that is smaller than the whole domain?

Can it be proved either way? Given the sum totality of today’s mathematics (i.e. all its known principles put together), is it possible to pick between the above two alternatives *in general*?

A subsidiary question only if the alternative (ii) is possible: please supply an example, better so, it is of a kind wherein the initial profile is infinitely differentiable, e.g. the bump function .

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I was expecting answers to affirm instantaneous action at a distance. The first full answer to arrive [^] confirms this anticipation. However, it’s too late in the night to go and point out the Brownian movement-related objection to it. I will do it some time tomorrow. (It’s a mathematics forum. I am not too comfortable writing maths-related comments directly. I have to first translate my thoughts from physics to mathematics.) Also, tomorrow, I will come back here and decide on the fly whether to add the usual final section “A Song I Like,” or not. Also, I will add the tags to this post, tomorrow.

In the meanwhile, think about it and see if you wish to answer or have an interaction on this topic, at Math[s] StackExchange.

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**Update on 2 January 2013:** I have now begun interaction at the Maths StackExchange forum. Also, now am adding the following section (**even if I still go jobless**), and the post tags. Guess I will have to be back very soon with another post on this same topic. A sort of “layman’s” (at least an engineer’s) version of the problem, and my position about it. I often find that by loosening the demands of the *mathematical* rigor a bit (though not the rigor of the basic logic or thought), a layman’s version helps bring in more context more easily, and thereby is actually helpful in delineating issues—both problems and solutions—better. So I will attempt doing that in a next post.

**A Song I Like:
**(Hindi) “swapn jhade phool se, mit chubhe shool se…” (“karvan guzar gaya, gubaar dekhate rahe”)

Lyrics: Neeraj

Singer: Mohammed Rafi

Music: Roshan

[E&OE]

To avoid this, it is highly recommended that latex gloves be worn so as to take out all the risky elements in

regards to safety and cleanliness!!! Usually continuous massage for 25-30 minutes over a particular place like vertebrae

etc will help oil reach up to bones. The program will enable one tackle challenges such as the patient’s skepticism or bad attitudes towards given routine..

It can ease stiff joints and also aids circulation and digestion??? Designating that many therapists as lead and then strategically scheduling them in order to cover the entire work week would surely prove to be an ineffective solution if not a nearly impossible plan. The first instruction to parents with children undergoing therapy for stuttering is to make their home as conducive to communication and speaking as possible. But the trend has been changed in this modernize world and now i guess. I see the huge guys that need massage because their muscles are so hyper-tonic (chronically contracted), and at the opposite extreme, women over 40 that never worked out habitually throughout life and so their large back muscles and core muscles are weak, which causes low back or thoracic pain!!!

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Imagine finding your life story: a copiously documented and flawless recounting of every day of your life… right up until yesterday where it states that you died and abruptly reverts back to gibberish. If pi truly contains every possible string, then that story is in there, too. Now, imagine if it said you die tomorrow. Would you believe it, or keep searching for the next copy of your life story?

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