Nonlinear PDEs

1. Front Matter

   Pages i-xviii

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2. Overview of Mathematical Methods in Partial Differential Equations

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 1-18

3. Liouville Type Theorems for Elliptic Operators in Divergence Form

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 19-27

4. Blow-Up Boundary Solutions of the Logistic Equation

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 29-115

5. Singular Lane–Emden–Fowler Equations and Systems

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 117-165

6. Singular Elliptic Inequalities in Exterior Domains

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 167-210

7. Two Quasilinear Elliptic Problems

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 211-243

8. Some Classes of Polyharmonic Problems

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 245-266

9. Large Time Behavior of Solutions for Degenerate Parabolic Equations

   • Marius Ghergu, Vicenţiu D. Rǎdulescu

   Pages 267-286

10. Reaction-Diffusion Systems Arising in Chemistry

    • Marius Ghergu, Vicenţiu D. Rǎdulescu

    Pages 287-335

11. Pattern Formation and the Gierer–Meinhardt Model in Molecular Biology

    • Marius Ghergu, Vicenţiu D. Rǎdulescu

    Pages 337-367

12. Back Matter

    Pages 369-391

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The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations  and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.​

• 35-02, 49-02, 92-02, 58-02, 37-02, 35Qxx
• degenerate and singular phenomena
• mathematical biology
• partial differential equations
• population genetics

From the reviews:

“This is a unique treatise on the application of advanced nonlinear operator theory. … The importance of mathematics in biosciences is very well supported by a great number of detailed examples in the text. The book can used for advanced graduate courses as well as a reference for advanced researchers in applied sciences. The authors have accomplished a wonderful mathematical journey.” (Dhruba Adhikari, MAA Reviews, January, 2013)

“The purpose of this book is to introduce fundamental techniques that are used for modeling and mathematical analysis of problems arising in chemistry, biology or genetics. … The book concludes with the extensive bibliography (217 references) and a detailed index. It will be useful for researchers, graduate students and specialists working with partial differential equations and their applications in chemistry and biomathematics.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1227, 2012)

• School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland

  Marius Ghergu

• Simion Stoilow Mathematics Institute, Romanian Academy, Bucharest, Romania

  Vicenţiu D. Rӑdulescu

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