Asymptotic for solutions of nonlinear parabolic equation in two-dimensional whole spaces
Gao Yong-dong · 2007
This paper is concerned with the decay properties for solutions of the nonlinear parabolic equations in twodimensional whole spaces R2. With the aid of spectral decomposition methods and fractional powers of Laplace operator, the paper proves that if the initial data u0 only satisfies u0 ∈ L2(R2), then the solution in L2(R2) norm converges asymptotically to 0, i.e.‖u(t)‖L2(R2)→0, as t→∞.