Nonlinear Partial Differential Equations with Applications

  • Tomáš Roubíček

Part of the International Series of Numerical Mathematics book series (ISNM, volume 153)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Tomáš Roubíček
    Pages 1-27
  3. Steady-State Problems

    1. Front Matter
      Pages 29-29
    2. Tomáš Roubíček
      Pages 31-93
    3. Tomáš Roubíček
      Pages 95-114
    4. Tomáš Roubíček
      Pages 115-131
    5. Tomáš Roubíček
      Pages 133-170
    6. Tomáš Roubíček
      Pages 171-198
  4. Evolution Problems

    1. Front Matter
      Pages 199-199
    2. Tomáš Roubíček
      Pages 201-211
    3. Tomáš Roubíček
      Pages 303-333
    4. Tomáš Roubíček
      Pages 335-349
    5. Tomáš Roubíček
      Pages 351-391
    6. Tomáš Roubíček
      Pages 393-448
  5. Back Matter
    Pages 449-476

About this book


This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook.


The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.


The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (…) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world.

(Mathematical Reviews)


abstract monotone-type operators including pseudomonotone ones accretive operators differential equations of elliptic and parabolic types quasilinear equations semilinear equations systems of partial differential equations various applications in continuum mechanics and thermodynamics

Authors and affiliations

  • Tomáš Roubíček
    • 1
  1. 1., Mathematical InstituteCharles UniversityPraha 8Czech Republic

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