Stabilization of a class of semilinear degenerate parabolic equations by Ito noise

We investigate the effect of Ito noise on the stability of stationary solutions to a class of semilinear degenerate parabolic equations with the nonlinearity satisfying an arbitrary polynomial growth condition. We will show that an Ito noise of sufficient intensity will stabilize the unstable stationary solution.

On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

The reaction diffusion system with anomalous diffusion and a balance lawut+-Δα/2u=-fu,v, vt+-∆β/2v=fu,v,0<α,β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction termfwhen0<α≤β≤2; (ii) no growth condition is imposed on the reaction termfwhen0<β≤α≤2.