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On one-dimensional semi-linear wave equations with null conditions

PDE and Applied Math Seminar

Speaker: Kevin Luli, UC Davis
Location: 3106 MSB
Start time: Thu, Jan 11 2018, 2:10PM

It is well-known that in dimensions at least three, semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such results still hold for a certain class of quasi-linear wave equations with null conditions. The proofs are based on the decay mechanism of linear waves. However, in one dimension, waves do not decay. Nevertheless, we will prove that small data still lead to global solutions if the null condition is satisfied. This is a joint work with S. Yang and P. Yu