Anomalies in Partial Differential Equations

This volume presents expert insights on partial differential equations, exploring linear and nonlinear models, critical phenomena, and applications in various fields.

The volume titled Anomalies in Partial Differential Equations features contributions from leading experts who presented their research at the INDAM Workshop held in September 2019 at the Istituto Nazionale di Alta Matematica, Università di Roma 'La Sapienza'. These contributions are expanded versions of their talks and cover a range of topics related to well-posedness and local solvability for linear models characterized by low regular coefficients.

In addition to linear models, the book delves into nonlinear dispersive models, such as damped waves and p-evolution models. The discussions focus on critical exponents, blow-up phenomena, and decay estimates for Sobolev solutions, providing a comprehensive view of the field. The authors explore various applications, including traffic flow models, Einstein-Euler systems, and stochastic partial differential equations, highlighting the practical implications of their theoretical findings.

The volume is rounded out with several contributions from the realms of Harmonic and Time-Frequency Analysis. Here, authors investigate the actions of localizing operators and describe wave front sets, enriching the discussion and offering new insights into the behavior of partial differential equations. Overall, Anomalies in Partial Differential Equations serves as a significant resource for researchers and practitioners interested in the complexities of modern mathematical analysis.