PDE Seminar Existence of Solutions with Moving Singularities for a Semilinear Parabolic Equation

2007-11-26 16:30 - 2007-11-26 17:30
Faculty of Science Building #8 Room 309
Shota SATO (Tohoku Univ.)
We consider singular solutions of some semilinear parabolic equation.Under some condition, there exists a singular steady state, which holdsa spatial singularity for all time. However, the existence of solutionswhose singularity moves depending on time has not been examined so far.In this talk, we establish time-local existence of a solution with amoving singularity for a certain class of itiatial data. Then we noticethat some critical exponent plays a crucial role. This is a joint workProf. Eiji Yanagida.