Дифференциальные уравнения в частных производных

London: Dover Publications, 2005. — 368 p. This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of...

Springer, 2016. — 587 p. — ISBN: 3319489348. This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier...

2nd edition. — Springer, 2021. — 270 p. — ISBN 978-3-030-81264-5. This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry...

Springer, 2018. — 230 p. — (Universitext). — ISBN: 3319783890. This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear...

Birkhäuser, 2021. — 669 p. — (Frontiers in Mathematics: Frontiers in Elliptic and Parabolic Problems). — ISBN 978-3030602192. This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by...

Springer International Publishing AG, 2018. — 240 p. — (Progress in Nonlinear Differential Equations and Their Applications: Subseries in Control 90). — ISBN: 3319766651. This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear...

Springer, 2019. — 455 p. — (Computational Methods in Applied Sciences 47). — ISBN: 3319783246. This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau,...

Springer, 2019. — 131 p. — (SpringerBriefs in Mathematics). — ISBN: 978-3-030-27229-6. This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola...

Springer, 2021. — 120 p. — (Springer Briefs in Mathematics). — ISBN 978-3030693480. This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the...