This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years. An update of Ramon Moore s previous books on the topic, it provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis. The authors provide a hands-on introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB. Readers will find the following features of interest: elementary motivating examples and notes that help maximize the reader s chance of success in applying the techniques; exercises and hands-on MATLAB-based examples woven into the text; INTLAB-based examples and explanations integrated into the text, along with a comprehensive set of exercises and solutions, and an appendix with INTLAB commands; an extensive bibliography and appendices that will continue to be valuable resources once the reader is familiar with the subject; and a Web page with links to computational tools and other resources of interest. Audience: Introduction to Interval Analysis will be valuable to engineers and scientists interested in scientific computation, especially in reliability, effects of roundoff error, and automatic verification of results. The introductory material is particularly important for experts in global optimization and constraint solution algorithms. This book is suitable for introducing the subject to students in these areas. Contents: Preface; Chapter 1: Introduction; Chapter 2: The Interval Number System; Chapter 3: First Applications of Interval Arithmetic; Chapter 4: Further Properties of Interval Arithmetic; Chapter 5: Introduction to Interval Functions; Chapter 6: Interval Sequences; Chapter 7: Interval Matrices; Chapter 8: Interval Newton Methods; Chapter 9: Integration of Interval Functions; Chapter 10: Integral and Differential Equations; Chapter 11: Applications; Appendix A: Sets and Functions; Appendix B: Formulary; Appendix C: Hints for Selected Exercises; Appendix D: Internet Resources; Appendix E: INTLAB Commands and Functions; References; Index.

Introduction to Interval Analysis

Linear Evolutionary Problems Hidden Regularity Weak Solutions Uniqueness Theorems Exact Controllability Hilbert Uniqueness Method Norm Inequalities New Uniqueness and Exact Controllability Results Dissipative Evolutionary Systems Linear Stabilization Nonlinear Stabilization Internal Stabilization of the Korteweg-de Vries Equation.

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Exact controllability and stabilization: The multiplier method

Preface 1. Fourier series and Fourier transforms 2. Distributions 3. Elliptic equations (fundamental theory) 4. Initial value problems (Cauchy problems) 5. Evolution equations 6. Hyperbolic equations 7. Semi-linear hyperbolic equations 8. Green's functions and spectra Supplementary remarks Guide to the literature Bibliography Symbols Index.

The theory of partial differential equations

CONTENTSIntroduction Chapter I. Existence and uniqueness of generalized solutions of the Cauchy problem and of initial boundary-value problems ??1.1. Theorems of existence and non-existence ??1.2. Uniqueness theorems Chapter II. Estimates and differential properties of generalized solutions ??2.1. The character of the dependence on the data ??2.2. Regularity and non-regularity Chapter III. Behaviour of generalized solutions for small values of time ??3.1. Finite rate of propagation of perturbations ??3.2. Inertia ??3.3. Shrinking of the size of the support Chapter IV. Behaviour of generalized solutions for large values of time ??4.1. Stabilization in finite time ??4.2. Localization of perturbations ??4.3. Asymptotic formulae References

http://iopscience.iop.org/article/10.1070/RM1987v042n02ABEH001309/pdf

Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations

In this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping. The equation that models this problem is given by \begin{eqnarray} u_{tt} - \kappa_0 \Delta u+{\int_0^t\, }{{\mbox{div}} [a(x)g(t-s)\nabla u(s)]ds} +f(u) +b(x)h(u_t)=0 \ &\mbox{in}& \ \Omega\times\Bbb R^+,\quad \end{eqnarray} where $a,b$ are nonnegative functions, $a\in C^1(\overline{\Omega})$, $ b\in L^{ \infty}(\Omega)$, satisfying the assumption \begin{eqnarray} a(x)+ b(x) \geq \delta > 0 \quad \forall x \in \Omega, \end{eqnarray} and f and h are power-like functions.
We observe that the assumption (0.2) gives us a wide assortment of possibilities from which to choose the functions a(x) and b(x), and the most interesting case occurs when one has simultaneous and complementary damping mechanisms. Taking this point of view into account, a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily "strategically localized dissipations" as considered in the prior literature.

Frictional versus Viscoelastic Damping in a Semilinear Wave Equation

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A difference inequality and its application to nonlinear evolution equations

Decay of solutions of the wave equation with a local nonlinear dissipation

Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations

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Mitsuhiro Nakao

Papers

A difference inequality and its application to nonlinear evolution equations

Decay of solutions of the wave equation with a local nonlinear dissipation

Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations

On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term

Decay of solutions of some nonlinear evolution equations