题目: Well posedness of nonlinear parabolic systems beyond natural duality
报告人：Miroslav Bulicek, Charles Univaersity in Prague
摘要: We develop a methodology for proving well-posedness in optimal
regularity spaces for a wide class of nonlinear parabolic
initial-boundary value systems, where the standard monotone operator
theory fails, namely for the situation when the nonlinear elliptic
operator is monotone and has linear growth at infinity.
The existence, uniqueness and regularity results by now are standard
whenever the right hand side belongs to the correpsonding negative
Sobolev space. However, even if the formal a priori estimates are
available, the existence and the uniqueness results was essentially
missing. We overcome the related crucial difficulty, namely lack of the
standard duality pairing, by resorting to proper weighted spaces and
consequently provide existence, uniqueness and optimal regularity. As a
consequence, we also obtain the uniqueness result for parabolic systems
when the right hand side is just a Radon measure.