Math 741. Topics in Partial Differential Equations: Blow-up for nonlinear wave equations.
- Fall 22 -
Hans Lindblad
I will teach a topics class in PDE, mostly going over some recent blow-up
results for nonlinear wave equations by Merle and others.
Many interesting equations from Physics can be written as systems of
Nonlinear wave equations. One can always show that these have local
solutions for some time. The ultimate goal for many physical equations is
to prove existence of global solutions for all times. However, apart from
in special cases such as small perturbations around a steady state one can
not not prove that there are global solutions. In fact the solutions may
develop singularities or blow up at some finite time, after which no regular
solution exist anymore. This blow-up can either be a real phenomena in nature,
such as development of black holes in general relativity or it can be an
indication that nature is non longer accurately described by the model.
In either case we would like to avoid blow-up.
It is therefore important to study how blow-up can occur for nonlinear
wave equations.
The lectures are MW 1.30-2.45 in Krieger 406.
wk |
date |
Monday |
Wednesday |
Friday |
1 |
8/29 |
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2 |
9/5 |
Holiday |
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3 |
9/12 |
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4 |
9/19 |
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5 |
9/26 |
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6 |
10/3 |
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7 |
10/10 |
moved to Tuesday 10/11 |
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8 |
10/17 |
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9 |
10/24 |
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10 |
10/31 |
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11 |
11/7 |
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12 |
11/14 |
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13 |
11/21 |
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No Class |
No Class |
14 |
11/28 |
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