Anomalies in Partial Differential Equations

The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability  for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of  critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in  the action of localizing operators or the description of wave front sets, complete the volume.

Table of Contents:
Ascanelli, A. and Cappiello, M., Semilinear p-evolution equations in weighted Sobolev spaces.- Ascanelli, A. et al.,   Random-field Solutions of Linear Parabolic Stochastic Partial Dierential Equations with Polynomially Bounded Variable Coefficients.- Brauer, U. and Karp, l., The non–isentropic Einstein–Euler system written in a symmetric hyperbolicfor.- Chen, W. and Palmieri, A., Blow–up result for a semilinear wave equation with a non linear memory term.- Ciani, S. and Vespri, V., An Introduction to Barenblatt Solutions for Anisotropic p-Laplace Equation.- Colombini, F. et al., No loss of derivatives for hyperbolic operators with Zygmund-continuous coecients in time.- Cordero, E., Note on the Wigner distribution and Localization Operators in the quasi-Banach setting.- Corli, A. and Malaguti, E., Wavefronts in traffic flows and crowds dynamics.- D’Abbicco, M., A new critical exponent for the heat and damped wave equations with non linear memory and not integrable data.-  Anh Dao, T. and Michael. R., Blow-up results for semi-linear structurally damped σ-evolution equation.- Rempel Ebert, M. and Marques, J. Critical exponent for a class of semi linear damped wave equations with decaying in time propagation speed.- Federico, S., Local solvability of some partial differential operators with non-smooth coefficients.- G. Feichtinger, A. et al., On exceptional times for point wise convergence of integral kernels in Feynman-Trotter path integral.-  Girardi, G. and Wirth, J., Decay estimates for a Klein–Gordon model with time-periodic coefficients.- Thieu Huy, N., Conditional Stability of Semigroups and Periodic Solutions to Evolution Equations.- Oberguggenberger, M., Anomalous solutions to non linear hyperbolic equations.- Rodino, L., and Trapasso, S.I., An introduction to the Gabor wave front set.- Sickel, W., On the Regularity of Characteristic Functions.- Yagdjian, K. et al., Small Data Wave Maps in Cyclic Spacetime