Дифференциальные уравнения в частных производных

Journal of Differential Equations 253 (2012) 2474–2492 This paper is concerned with weak solutions of the degenerate diffusive Hamilton–Jacobi equation with Dirichlet boundary conditions in a bounded domain Ω ⊂ RN , where p > 2 and q > p −1. With the goal of studying the gradient blow-up phenomenon for this problem, we first establish local well-posedness with blow-up alternative...

World Scientific Publishing Company, 2002. - 504 pages. Proceedings of the 4th European Conference held June 18-22, 2001 in Rolduc, Netherlands, and September 24-28, 2001 in Gaeta, Italy. For graduate students and researchers in the fields of partial differential equations and applied mathematics.

Springer-Verlag, 2012. - 376 pages. The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an...

Journal of Differential Equations 253 (2012) 2140–2160 In this paper, we consider fully nonlinear elliptic equations related to Yamabe problem. We improve a result of Jin, Li and Xu and establish the existence and nonexistence for positive entire subsolutions with a generalized Keller–Osserman condition.

Birkhauser, 2011. — 375 p. — ISBN: 3034800681 The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential...

Journal of Computational Physics 231 (2012) 2245–2258 In Zhang and Shu (2010) [20], Zhang and Shu (2011) [21] and Zhang et al. (in press) [23], we constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. In this paper, we present an...