Contains thirteen papers devoted to recent results in mathematics, focusing on nonlinear partial differential equation and applications

Preface.- On effective PDEs of quantum physics.- Critical exponents for differential inequalitieswith Riemann-Liouville and Caputo fractional derivatives.- Weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms and different power nonlinearities.- Incompressible Limits for Generalisations to Symmetrisable Systems.- The critical exponent for evolution models with power non-linearity.- Blow-up or global existence for the fractional Ginzburg-Landau equation in multi-dimensional case.- Semilinear damped Klein-Gordon models with time-dependent coefficients.- Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term.- 4D semilinear weakly hyperbolic wave equations.- Smoothing and Strichartz estimates to perturbed Magnetic Klein-Gordon equations in exterior domain and some applicationsv.- The Cauchy problem for dissipative wave equations with weighted nonlinear terms.- Global existence results for a semilinear wave equation with scale-invariant damping and mass in odd space dimension.- Wave equations in modulation spaces-Decay versus loss of regularity.