Science Daily writes Mathematicians solve 140-year-old Boltzmann equation.
"Pennsylvania mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases."
"Using modern mathematical techniques from the fields of partial differential equations and harmonic analysis -- many of which were developed during the last five to 50 years, and thus relatively new to mathematics -- the Penn mathematicians proved the global existence of classical solutions and rapid time decay to equilibrium for the Boltzmann equation with long-range interactions. Global existence and rapid decay imply that the equation correctly predicts that the solutions will continue to fit the system's behavior and not undergo any mathematical catastrophes such as a breakdown of the equation's integrity caused by a minor change within the equation. Rapid decay to equilibrium means that the effect of an initial small disturbance in the gas is short-lived and quickly becomes unnoticeable."
3 comments:
Here is to science and all its wonders! I majored in differential equations and wrote my masters' thesis on a special (odnorodnie?) kind of them. Yet I've never heard of partial differential equations, they must be new. It's simply amazing how even mathematics, stable as they are, keep getting richer, old theorems get proved for new dimensions (see Grisha Perelman's achievement) etc. I guess I'm somewhat overwhelmed.
I suspect the terminology was just different in Russian. My college advanced calculas book, circa 1975, (yes, I still have it) has a chapter on partial differentiation and I don't think it was recent then. Apparently I understood it at the time since I had underlined several passages.
You must be right. Maybe I should buy an advanced calculus book and learn all the English names or else I'll continue being overwhelmed for no reason...then again, it's more fun this way.
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