带有局部化源的弱耦合退化奇异抛物型方程组解的爆破性

在齐次狄利克雷边界条件下讨论了带有局部化源的弱耦合退化奇异抛物型方程组ut-(xaux)x=emu(x0(t),t)+nv(x0(t),t),vt-(xβvx)x=epu(x0(t),t)+qv(x0(t),t)的爆破性,其中x0(t)∶R+→(0,a)是H(o)lder连续的,T≤..,a(a＞0)是常数,m、n、p...

Global existence and blow-up for parabolic system with localized source

In this paper, we discuss the following weakly coupled degenerate and singular parabolic equations with localized source u_t-(x^αu_x)_x=e^{m u(x_<sup>0}(t),t)+n v(x_<sup>0(t),t), v_t-(x^βv_x)_x=e^{p u(x_<sup>0}(t),t)+q v(x_<sup>0(t),t) in(0,a)×(0,T)with homogeneous Dirichlet boundary conditions, where x₀(t):R⁺→(0,a)is Hölder continuous, T≤∞, a(a>0)are constants, m,n,p,q are positive real numbers and α,β∈[0,2). The existence of a unique classical non -negative solution is established and the sufficient conditions for the solution that blow -up in finite time are obtained. We also obtain the blow -up rate under the condition α=β.