The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Monday November 5 in K3 from 9:00 till 10:30.
Speaker: Miroslav Bulíček
Title: Well posedness of nonlinear parabolic systems beyond natural duality
Abstract:
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 corresponding 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.