Titlebook: New Tools for Nonlinear PDEs and Application; Marcello D‘Abbicco,Marcelo Rempel Ebert,Tohru Ozaw Book 2019 Springer Nature Switzerland AG

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Marcello D‘Abbicco,Marcelo Rempel Ebert,Tohru OzawContains thirteen papers devoted to recent results in mathematics, focusing on nonlinear partial differential equation and applications.Provides contributions about qualitative properties of solutions

ARBOR

On Effective PDEs of Quantum Physics,The Hartree-Fock equation is a key effective equation of quantum physics. We review the standard derivation of this equation and its properties and present some recent results on its natural extensions – the density functional, Bogolubov-de Gennes and Hartree-Fock-Bogolubov equations. This paper is based on a talk given at ISAAC2017.

谷物

The Critical Exponent for Evolution Models with Power Non-linearity,In this note we derive ..???.. estimates for the solutions to the Cauchy problem . with .?>?1. Moreover, we derived the critical index ..(.) for the existence of global in time small data solutions to the associated semilinear Cauchy problem with power nonlinearity |.|., .?>?1.

不近人情

4D Semilinear Weakly Hyperbolic Wave Equations,In this paper we exploit the 4Dimensional weakly hyperbolic equation . We establish a global existence of radial solutions in a subcritical range of .. This range depends on the zero of .(.) and .(.). In particular we deal with . and . with .., ..?≥?0. In the case ..?=?2 the radial assumption can be omitted.

PAC

Smoothing and Strichartz Estimates to Perturbed Magnetic Klein-Gordon Equations in Exterior Domain This paper is based on the talk of the first author at ISAAC Congress 2017 at V?xj?, Sweden. We deal with the smoothing and Strichartz estimates to magnetic Klein-Gordon equations with time-dependent perturbations in exterior domain. Also, the smoothing estimates are applied to establish a scattering of solutions for small perturbations.

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