Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications

ISBN-13: 9780367387594 / Angielski / Miękka / 2019 / 336 str.

Janusz Mierczynski; Wenxian Shen

Opis

Containing many new results and considering existing results from a fresh perspective, this clear, unified, and self-contained book focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The authors prove that time dependence and randomness do not reduce the principal spectrum and Lyapunov exponents of nonautonomous and random parabolic equations. They also address classical Faber–Krahn inequalities for elliptic and time-periodic problems and extend the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems. The final chapter presents applications to Kolmogorov systems of parabolic equations.

Spis treści

Introduction. Fundamental Properties in the General Setting. Spectral Theory in the General Setting. Spectral Theory in Nonautonomous and Random Cases. Influence of Spatial-Temporal Variations and the Shape of Domain. Cooperative Systems of Parabolic Equations. Applications to Kolmogorov Systems of Parabolic Equations. References. Index.

O autorze

Mierczynski, Janusz; Shen, Wenxian