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The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern-Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers.The proceedings have been selected for coverage in:* Index to Scientific & Technical Proceedings (R) (ISTP (R) / ISI Proceedings)* Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)* CC Proceedings - Engineering & Physical Sciences