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- W2073810833 abstract "In this paper we utilize the method of invariant set to derive exact solutions of the two-dimensional nonlinear reaction–diffusion equations with source term. It is shown that there exists a class of reaction–diffusion equations which are invariant with respect to the sets E1={u:ux=vxf(t)F(u),uy=vyf(t)F(u)} and E2={u:ux=a′(x)f(t)F(u),uy=b′(y)g(t)F(u)}, with f≠g. As a result, we obtain exact solutions of the certain nonlinear reaction–diffusion equations. These solutions extend the well-known self-similar solutions and instantaneous source type solutions of the porous medium equation. The behavior to some solutions and the corresponding interfaces are also described." @default.
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- W2073810833 date "2009-12-01" @default.
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- W2073810833 title "Invariant sets and solutions to the two-dimensional nonlinear reaction–diffusion equations" @default.
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- W2073810833 doi "https://doi.org/10.1016/j.na.2009.01.102" @default.
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