Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern-Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers. The proceedings have been selected for coverage in:. Index to Scientific & Techn

Differential equations, Elliptic --- Differential equations, Parabolic --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.

Differential equations, Parabolic. --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.

Adaptive control systems. --- Differential equations, Parabolic. --- Distributed parameter systems. --- Self-adaptive control systems --- Systems, Distributed parameter --- Parabolic differential equations --- Parabolic partial differential equations --- Artificial intelligence --- Feedback control systems --- Self-organizing systems --- Control theory --- Engineering systems --- System analysis --- Differential equations, Partial

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field.

Attractors (Mathematics) --- Differential equations, Parabolic. --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems --- Differential equations, Parabolic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Differential equations, Elliptic --- Differential equations, Parabolic --- Differential equations, Elliptic. --- Differential equations, Parabolic. --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear