Using a mixed jump and diffusion model, we compute the time and energy needed to find an object placed at a finite distanceD from a searcher’s initial location within an infinite non-homogenous search space, assuming that the searcher has imprecise information about where and how to search, and also that the searcher may be blocked or destroyed during the search. This problem arises in large wired or wireless networks with imprecise routing tables and packet losses [4, 8, 10, 13], in large databases with uncertain or approximately represented data such as the content of images [5, 14], and in the search by robots in hostile environments such as minefields [7]. Introduction An animal’s search for prey was modelled in [9, 12] when the predator renews its energy reserve during the search. Randomly connected finite graphs in [11] represent search in a computer network or a system of roads. In [10] it was shown that the time it takes a data packet to travel from a source to a destination node in an infinitely large and unreliable network is finite on average, if a timeout mechanism destroys the packet after a predetermined time, replacing it with a new one that starts at the source proceeding at random and independently of its predecessor. This was generalised [15] to N searchers which are simultaneously, but independently sent out in the quest for the same object. Most of the literature considers homogenous search spaces, and in this paper we develop a mixed analytical-numerical method for an infinite random nonhomogenous medium that generalises the work in [15] obtaining expressions for the average time and energy that it takes the searcher to eventually find the object it is seeking. An interesting phase transition is exhibited concerning the eventual success of the search depending on the relative speed of approach of the searcher and the intensity of events which block the searcher’s progress. The Model Although traditionally most models in computer systems and networks are discrete [3], here we consider a continuous distance Y (t) of the searcher to the object at time t ≥ 0. The searcher starts at Y (0) = D and the search ends at time T = inf{t : Y (t) = 0}. If the random variable s(t) represents the state of the searcher, s(t) ∈ {S,W,P, ...}, then s(t) ∈ S if the search is proceeding with the search and its distance from the destination is Y (t) > 0. The probability density function of Y (t) is denoted f(z, t)dz = P [z 0} the following events can occur in the time interval [t, t+Δt[. With probability λ(z)Δt + o(Δt) the searcher is destroyed or lost, and enters state L. From that state it enters state W after an exponentially distributed delay of parameter r. With probability rΔt + o(Δt) the searcher’s life-span runs out and it enters state W. Note that 1/r is the average life-span. As indicated earlier, when it enters state W, after an additional delay of average value 1/μ, the searcher is replaced with a new one at the source. The average rate per unit time at which the searcher approaches the object being sought when it is at distance z is b(z), and the variance of the distance travelled in the interval [t, t+Δt[ is denoted by