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Functional analysis --- Differential equations, Partial

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Nonlinear wave equations --- Differential equations, Partial

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Computational fluid dynamics --- Differential equations, Partial --- Finite element method

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If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical analysis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.

Reaction-diffusion equations --- Differential equations, Elliptic --- Numerical solutions. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Differential equations, Parabolic --- Differential equations, partial. --- Partial Differential Equations. --- Partial differential equations --- Partial differential equations. --- Mathematics --- Differential equations, Partial

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This textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrations it introduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.

Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Partial differential equations --- Differential equations, Partial - Textbooks --- Boundary value problems for evolution and stationary equations. --- Diffusion equation. --- Integral transforms. --- Laplace and Poisson equation. --- Partial differential equation. --- Wave equation.