Progress in Partial Differential Equations

Vol. 44. Springer, 2013.

Научный редактор: M. Reissig

Ответственный редактор: M. Ruzhansky

Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material.

The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

Главы книги

On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data

Никитин А. А., , in: Progress in Partial Differential EquationsVol. 44.: Springer, 2013. Ch. 10 P. 223–238.

In the present paper we study the boundary control by the third boundary condition on the left end of a string, the right end being fixed. An optimality criterion based on the minimization of an integral of a linear combination of the control itself and its antiderivative raised to an arbitrary power p≥1 is established. A ...

Добавлено: 28 сентября 2013 г.

Ключевые слова: Asymptotic Profiles, Regularity and Well-Posedness