PDE Seminar A remark on the asymptotic behavior of time global solutions for a semilinear parabolic equation involving critical Sobolev exponent

2007-12-10 16:30 - 2007-12-10 17:30
Faculty of Science Building #8 Room 309
Michinori Ishiwata (Muroran Institute of Technology)
In this talk, we are concerned with the asymptotic behavior oftime global solutions for a semilinear parabolic equation involvingcritical Sobolev exponent. In the subcritical case, it is known thatif the initial data is nonnegative and sufficiently small (resp. large),then the solution exists globally in time and converges to the trivialstationary solution (resp. blows up in finite time). Moreover, theasymptotics of solutions which emanate from middle-size initial datais also known. On the other hand, in the critical case, not so much isknown so far. In this talk, we shall discuss the bubbling phenomena forglobal-in-time solutions in the critical case and clarify the structureof the space of initial data.