New Tools for Nonlinear PDEs and Application

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.

Contains thirteen papers devoted to recent results in mathematics, focusing on nonlinear partial differential equation and applications Provides contributions about qualitative properties of solutions of linear and nonlinear models, well-posedness results, results on asymptotic profiles of solutions, on blow-up behavior and on the influence of low regular coefficients

Inhalt
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.