Distributional Nonlinear Wave Equations: Well-Posedness and Stabilizability

Khaled Zennir · Svetlin G. Georgiev

2025年1月 · De Gruyter Series in Nonlinear Analysis and Applications 第 45 本图书 · Walter de Gruyter GmbH & Co KG

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The book contains eleven chapters introduced by an introductory description. Qualitative properties for the semilinear dissipative wave equations are discussed in Chapter 2 and Chapter 3 based on the solutions with compactly supported initial data. The purpose of Chapter 4 is to present results according to the well-possednes and behavior f solutions the nonlinear viscoelastic wave equations in weighted spaces. Elements of theory of Kirchhoff problem is introduced in Chapter 5. It is introduced same decay rate of second order evolution equations with density. Chapter 6 is devoted on the original method for Well posedness and general decay for wave equation with logarithmic nonlinearities. In Chapter 7, it is investigated the uniform stabilization of the Petrovsky-Wave nonlinear coupled system. The question of well-posedness and general energy decay of solutions for a system of three wave equations with a nonlinear strong dissipation are investigated in chapter 8 using the weighied. In sofar as Chapter 9 and chapter 10 are concerned with damped nonlinear wave problems in Fourier spaces. The last Chapter 11 analysis the existence/ nonexistence of solutions for structural damped wave equations with nonlinear memory terms in Rn.

作者简介

Khaled Zennir: was born in Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. professor). He is now associate Professor at Qassim University, KSA. His research interests lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence, Blow-Up, and Long Time Behavior.

Svetlin G. Georgiev: (born 05 April 1974, Rouse, Bulgaria) is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales.