Semilinear hyperbolic equations

Semilinear hyperbolic equations by Vladimir Georgiev Download PDF EPUB FB2

Wave equations 2 Heat equations 3 NLS equations 3 Open problems 5 2. Semilinear hyperbolic equation 6 Low initial energy 10 Critical initial energy 14 High initial energy 15 3.

Semilinear parabolic equation 18 Low initial energy 18 Critical initial energy 22 High initial energy 24 4. Nonlinear. The purpose of this paper is to obtain the regularity for solutions of semilinear neutral hyperbolic equations with the nonlinear convolution.

The principal operator is the infinitesimal generator of a cosine and sine families. In order to show a variation of constant formula for solutions, we make of using the nature of cosine and sine : Seong-Ho Cho, Jin-Mun Jeong. Semilinear Hyperbolic Equations Dirichlet Problem Kaplan's Method Nonnegative Global Solution Ordinary Differential Inequality These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be Cited by: 1. “This book is a valuable reference book for specialists in the field and an excellent graduate text giving an overview of the literature on solutions of semilinear elliptic equations.

the book should be strongly recommended to anyone, either graduate student or researcher, who is interested in variational methods and their applications to.

Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for Semilinear hyperbolic equations book archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory.

the case of equation () on 3D torus, the n ormally-hyperbolic IM is constructed Semilinear hyperbolic equations book the case ω 6 = 0 (see [19]) although as known for a long time (see [34]) such an object may not exist in the.

QUENCHING OF SOLUTIONS OF NONLINEAR HYPERBOLIC EQUATIONS WITH DAMPING JIANMIN ZHU A hyperbolic initial-boundary value problem with nonlinear damping and singular boundary value problem for a semilinear heat equation.

Chang and Levine [4]extended the concept to a first initial-boundary value problem for a semilinear wave equation in. () On the quenching behaviour of a semilinear wave equation modelling MEMS technology.

Discrete and Continuous Dynamical Systems() Hyperbolic quenching problem with damping in the micro-electro mechanical system device. This paper is concerned with the study of local decay rates of the energy associated to a semilinear wave equation in an inhomogeneous medium with frictional localized damping.

The problem is consi. Book Description. Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations.

The authors present a unified approach to deal with these quasilinear PDEs. SOLUTION QUENCHING OF SEMILINEAR HYPERBOLIC EQUATIONS thatif e is "large" u quenchesinfinite timewhereasin 4weshowthatif e is "small", u cannot quench at all, even in infinite time. In 5 wediscuss the behavior of u as e--> 0+" Weconcludewithsomeremarksin the final section.

The definition of a weak solution. Wesay u is a weak solution of. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions.

The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations. Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences.

The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a. Journals & Books; Register Sign in. Vol Is 15 JunePages On potential wells and applications to semilinear hyperbolic equations and parabolic equations.

[1] Moncef Aouadi, Alain -stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations & Control Theory,4 (3): doi: /eect [2]. On Weak Solutions of Semilinear Hyperbolic-Parabolic Equations Article (PDF Available) in International Journal of Mathematics and Mathematical Sciences 19(4) January with Reads.

A weak asymptotic solution analysis for a Lagrangian-Eulerian scheme for scalar hyperbolic conservation laws Eduardo Abreu, Wanderson Lambert, John P´erez and Arthur Santo Decay in L∞for the damped semilinear wave equation on a bounded.

This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed.

Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear. Merle, H.; Zaag. On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations.

Communications in Mathematical Physics, (3),N. Mizoguchi. Type-II blowup for a semilinear heat equation.Adv. Differential Equations, 9(), N. Mizoguchi. FOR SEMILINEAR HYPERBOLIC EQUATIONS AND PARABOLIC EQUATIONS WITH CRITICAL INITIAL DATA By XU RUNZHANG College of Science,HarbinEngineeringUniversity,People’sRepublicof China Abstract.

We study the initial boundary value problem of semilinear hyperbolic equations u tt −Δu = f(u) and semilinear parabolic equations u t −Δu = f(u) with. The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs.

Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis.

Compared to other.An Abstract Semilinear Hyperbolic Volterra lntegrodifferential Equation MELVIN L. HEARD Department ~JMathematics, UniversitJ~ of Illinois at Chicago Circle, Chicago, Illinois Submitted bv K. L. Cooke We consider semilinear integrodifferential equations of the form u’(f) + A(t) u(t) = j; g(t.

s. Journals & Books; Help We consider the Cauchy problem for the semilinear wave equation. The Cauchy data are assumed to be conormal with respect to a point, and the source term is polynomial with respect to the solution and its first derivatives.

Thanks to the study of multiplicative properties of some refined hyperbolic conormal space.