Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system

Exact Criterion for Global Existence and Blow Up to a Degenerate Keller-Segel System

A degenerate Keller-Segel system with diffusion exponent m with 2n n+2 < m < 2 − 2 n in multi dimension is studied. An exact criterion for global existence and blow up of solution is obtained. The estimates on L 2n n+2 norm of the solution play important roles in our analysis. These estimates are closely related to the optimal constant in the HardyLittlewoodSobolev inequality. In the case of in...

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Existence and Blow-up for a Nonlocal Degenerate Parabolic Equation

In this paper, we establish the local existence and uniqueness of the solution for the degenerate parabolic equation with a nonlocal source and homogeneous Dirichlet boundary condition. Moreover, we prove that the solution blows up in finite time and obtain the blow-up set in some special case. Mathematics Subject Classification: 35K20, 35K30, 35K65

Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation

Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources. MSC: 35B33, 35B40, 35K65, 35K55