Asymptotic behavior of solutions of a parabolic equations in a band domain
We consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions.We show that,under certain conditions,the solution u of the initial-boundary value problem tends to infinite as t →∞.Moreover,by using the zero number argument we show that for any x ≠ 0,ux(x,t)also tends as t →∞ to infinity,that is,the gradient is asymptotically unbounded.
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