This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
A self-contained book on parabolic problems with critical nonlinearities
Includes applications to the Navier-Stokes equations, the quasi-geostrophic equation, and reaction-diffusion systems
Of interest to researchers and graduate students alike
Tomasz W. Dłotko, University of Silesia in Katowice, Poland;
Yejuan Wang, Lanzhou University, P. R. China.