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Separation of time and space 
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#1
Dec2907, 10:48 AM

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In pde, it seems to me all kinds of equations about nature phenomena have the property that time and space derivatives are separate. For example, u_t = u_xx, heat equation. So I wonder, is that always the case in nature? I mean, do you guys ever see equation describing real nature mechanism but has mixed derivatives involved, ie, has a term like u_tx? If not, is there a reason for that?
This might be a silly question, but thanks in advance. 


#2
Dec2907, 11:00 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,553

It's not clear t me what you mean by "separate". Do you mean "no mixed derivatives", like u_xt?The heat equation in 3 space dimensions, [itex]u_t= u_{xx}+ u_{yy}+ u_{zz}[/itex] have the other space variables as "separate" as x and t. That depends entirely on your choice of coordinate system not "nature".



#3
Dec2907, 11:27 AM

P: 6




#4
Dec2907, 12:39 PM

P: 365

Separation of time and space



#5
Dec2907, 04:14 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,553




#6
Dec2907, 05:43 PM

P: 6




#7
Dec2907, 05:44 PM

P: 6




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