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SUMMARY:Junior Analysis Seminar – Oliver Gough (Bath)
DESCRIPTION:Title\n\nStable blow-up for semilinear wave equations with quad
 ratic derivative nonlinearities\n\nAbstract\n\nI will discuss two results 
 on stable finite-time blow-up for semilinear wave equations with quadratic
  derivative nonlinearities. In one dimension\, both the time-derivative an
 d spatial-derivative nonlinearities admit “generalised self-similar” b
 low-up solutions. I will begin by briefly reviewing a result on the constr
 uction and asymptotic stability of such solutions in the time-derivative c
 ase.\nThe main focus of the talk will be recent joint work with Manuel del
  Pino and Monica Musso extending this picture to the spatial-derivative no
 nlinearity in all dimensions n \\geq 2. Under radial symmetry\, we constru
 ct solutions that blow up on a sphere and establish their stability under 
 radial perturbations. I will explain how the one-dimensional analysis ente
 rs both the construction and the stability analysis\, and discuss the new 
 difficulties that arise in higher dimensions.\n\nPlease note that the semi
 nar will take place in person in room 140 of Huxley Building.\n\nClick her
 e to get to the Junior Analysis Seminar webpage.
URL:https://www.imperial.ac.uk/events/214960/junior-analysis-seminar-oliver
 -gough-bath/
DTSTART;TZID=Europe/London:20261014T140000
DTEND;TZID=Europe/London:20261014T150000
LOCATION:140\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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