On the finite dimension of attractors of parabolic problems in \(\mathbb R^N\) with general potentials (Q2474343)

The authors consider the nonlinear reaction-diffusion equations of the type \[ \partial_t u=\Delta_x u+ f(x,u)\quad\text{in }\mathbb{R}^N, \qquad u(0,x)= u_0(x) \] and study the finite dimensionality of the attractors. For a general potentials they obtain finite fractional dimensionality of the attractor. Moreover, in the case of linear potentials, the authors show that the potential may change sign and it does not need to be constant.