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.

Autorentext

Massimo Cicognani is Professor of Mathematical Analysis at the University of Bologna. His research field is regularity of solutions to PDEs of evolution type.

Daniele Del Santo is Professor of Mathematical Analysis at the University of Trieste. His research focuses on PDEs theory, in particular hyperbolic and parabolic equations with non regular coefficients.

Alberto Parmeggiani is Professor of Mathematics at University of Bologna. His research field is Analysis, more specifically the geometric theory of partial differential equations.

Michael Reissig is Professor of Partial Differential Equations at TU Bergakademie Freiberg. His research area is the theory of linear and nonlinear dispersive models.

Inhalt
Ascanelli, A. and Cappiello, M., Semilinear p-evolution equations in weighted Sobolev spaces.- Ascanelli, A. et al., Random-eld Solutions of Linear Parabolic Stochastic Partial Dierential Equations with Polynomially Bounded Variable Coefficients.- Brauer, U. and Karp, l., The nonisentropic EinsteinEuler system written in a symmetric hyperbolicfor.- Chen, W. and Palmieri, A., Blowup 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 ows 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 -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 KleinGordon 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