In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study properties of symplectic translating solitons. We prove that, the Kähler angle α of a symplectic translating soliton with max |A| = 1 satisfies that sup |α| > π 4 |T | |T |+1 where T is the direction in which the surface translates. Mathematics Subject Classification (2000): 53C44 (primary), 53C...

We obtain some blowup results of the Euler equations for Generalized Chaplygin Gas (GCG). In particular, we show that the solutions with velocity of the form u(t, x) = ȧ(t) a(t) x blow up on finite time if the parameter of the ordinary differential equation related to a(t) is negative. Moreover, by the substitution and perturbation methods, we construct a family of non-spherical symmetric blowu...

We prove gradient boundary blow up rates for ergodic functions in bounded domains related to fully nonlinear degenerate/singular elliptic operators. As a consequence, we deduce the uniqueness, constants, of functions. The results are obtained by means Liouville type classification theorem half-spaces infinite value problems nonlinear, uniformly

We construct a center-stable manifold of the ground state solitons in the energy space for the critical wave equation without imposing any symmetry, as the dynamical threshold between scattering and blow-up, and also as a collection of solutions which stay close to the ground states. Up to energy slightly above the ground state, this completes the 9-set classification of the global dynamics in ...

The blow-up rate estimate for the solution to a semilinear parabolic equation ut = ∆u+V (x)|u|p−1u in Ω×(0, T ) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x, 0) = Mφ(x) as M goes to infinity, which have been found in [5], are improved under some reason...

This paper concerns a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover it is proved that for a large class of initial data blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The ...

Abstract This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution to exist globally or blow up in finite time are obtained. Furthermore, under c...

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separ...

In the last twenty years, there have been significant advances in study of blow-up phenomenon for critical generalized Korteweg-de Vries equation, including determination sufficient conditions blowup, stability blowup a refined topology and classification minimal mass blowup. Exotic solutions with continuum rates multi-point were also constructed. However, all these results, as well numerical s...