  We study the trapping reaction-diffusion problem in a symmetric double well
potential in one dimension with a static trap located at the middle of the
central barrier of the double well. The effect of competition between the
confinement and the trapping process on the time evolution of the survival
probability is considered. The solution for the survival probability of a
particle is obtained by the method of Green's function. Furthermore, we study
trapping in the presence of a growth term. We show that for a given growth rate
there exist a threshold trapping rate beyond which the population can become
extinct asymptotically. Numerical simulations for a symmetric quartic potential
are done and results are discussed. This model can be applied to study the
dynamics of a population in habitats with a localized predation.
