Applied Wave Mathematics

1. Front Matter

   Pages I-XII

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2. CENS, CMA and the CENS-CMA Project

   • Jüri Engelbrecht, Ragnar Winther, Ewald Quak

   Pages 1-6

3. Waves in Solids

   1. Front Matter

      Pages 7-7

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   2. Overview

      • Arkadi Berezovski

      Pages 9-11

   3. Deformation Waves in Solids

      • Jüri Engelbrecht

      Pages 13-30

   4. The Perturbation Technique for Wave Interaction in Prestressed Material

      • Arvi Ravasoo

      Pages 31-53

   5. Waves in Inhomogeneous Solids

      • Arkadi Berezovski, Mihhail Berezovski, Jüri Engelbrecht

      Pages 55-81

4. Mesoscopic Theory

   1. Front Matter

      Pages 83-83

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   2. Overview

      • Wolfgang Muschik

      Pages 85-88

   3. Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids

      • Christina Papenfuss

      Pages 89-125

   4. Towards a Description of Twist Waves in Mesoscopic Continuum Physics

      • Heiko Herrmann

      Pages 127-145

5. Exploiting the Dissipation Inequality

   1. Front Matter

      Pages 147-147

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   2. Overview

      • Wolfgang Muschik

      Pages 149-151

   3. Weakly Nonlocal Non-equilibrium Thermodynamics – Variational Principles and Second Law

      • Péter Ván

      Pages 153-186

6. Waves in Fluids

   1. Front Matter

      Pages 187-187

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   2. Overview

      • Tarmo Soomere

      Pages 189-192

   3. Long Ship Waves in Shallow Water Bodies

      • Tarmo Soomere

      Pages 193-228

   4. Modelling of Ship Waves from High-speed Vessels

      • Tomas Torsvik

      Pages 229-263

   5. New Trends in the Analytical Theory of Long Sea Wave Runup

      • Ira Didenkulova

      Pages 265-296

7. Mathematical Methods

   1. Front Matter

      Pages 297-297

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This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

• Wave
• applied mathematics
• nonlinear wave equations
• numerical mathematics
• solids and fluids
• solitons
• wave equation
• partial differential equations

• Tallinn University of Technology, Inst. Cybernetics, Estonian Academy of Sciences, Tallinn, Estonia

  Ewald Quak, Tarmo Soomere

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