Advances in nonlinear partial differential equations and related areas : a volume in honour of Professor Xiaqi Ding

Kalman filtering algorithm gives optimal (linear, unbiased and minimum error-variance) estimates of the unknown state vectors of a linear dynamic-observation system, under the regular conditions such as perfect data information; complete noise statistics; exact linear modelling; ideal will-conditioned matrices in computation and strictly centralized filtering. In practice, however, one or more of the aforementioned conditions may not be satisfied, so that the standard Kalman filtering algorithm cannot be directly used, and hence "approximate Kalman filtering" becomes necessary. In the last decade, a great deal of attention has been focused on modifying and/or extending the standard Kalman filtering technique to handle such irregular cases. This book is a collection of several survey articles summarizing recent contributions to the field, along the line of approximate Kalman filtering with emphasis on its practical aspects Relaxation limits for a class of balance laws with kinetic formulation / Yann Brenier, Lucilla Corrias, and Roberto Natalini -- A note on the existence of multi-peaked solutions to a semilinear elliptic problem / Daomin Cao -- Large-time behavior of entropy solutions in L(infinity symbol) for multidimensional conservation laws / Gui-Qiang Chen and Hermano Frid -- Formation of shock waves in potential flow / Shu-Xing Chen amd Li-Ming Dong -- Indefinite elliptic problems with critical exponents / Wenxiong Chen and Congming Li -- An explicit example of stable and instable motions in fluid mechanics / Zhi-Min Chen -- Nonlinear diffusive-dispersive limits for multidimensional conservation laws / Joaquim M.C. Correia and Philippe G. LeFloch -- Two-pressure two phase flow / James Glimm, David Saltz, and David H. Sharp -- PlainleveМЃ analysis and its applications / Benyu Guo and Zhixiong Chen -- Stability of traveling wave solutions for a rate-type viscoelastic system / Ling Hsiao and Tao Luo -- Existence and uniqueness of discontinuous solutions for a class of nonstrictly hyperbolic systems / Feimin Huang -- Some results of the generalized solutions defined by Lebesgue-Stieltjes integral for hyperbolic conservation laws / Caizhong Li -- Generalized Rankine-Hugoniot relations of Delta-shocks in solutions of transportation equations / Jiequan Li and Tong Zhang -- Geometric measure of nodals and growth of solutions to elliptic equations / Fang Hua Lin -- A note on development of singularities of solutions of nonlinear hyperbolic partial differential equations / Longwei Lin -- Convergence of viscosity solutions to a nonstrictly hyperbolic system / Yun-Guang Lu -- Strange attractors in pseudospectral solutions of the dissipative Zakharov equations / Shuqing Ma, Qianshun Chang, and Xianghui Wu -- Elliptic problems with supercritical nonlinearity / Yaotian Shen and Shushen Yan -- Convergence of relaxing scheme for conservation laws / Jinghua Wang and Gerald Warnecke -- On half-space problems for the heat equations with nonlinear boundary conditions / Ming-Xin Wang and Shu Wang -- String-like defects and fractional total curvature in a gauged harmonic map model / Yisong Yang -- The Riemann problem for nonconvex combustion model from ZND to CJ theory / Peng Zhang and Tong Zhang -- Systems of conservation laws with incomplete sets of eigenvectors everywhere / Yuxi Zheng