  A notion of measure solution is formulated for a coagulation-diffusion
equation, which is the natural counterpart of Smoluchowski's coagulation
equation in a spatially inhomogeneous setting. Some general properties of such
solutions are established. Sufficient conditions are identified on the
diffusivity, coagulation rates and initial data for existence, uniqueness and
mass conservation of solutions. These conditions impose no form of monotonicity
on the coagulation kernel, which may depend on complex characteristics of the
particles. They also allow singular behaviour in both diffusivity and
coagulation rates for small particles. The general results apply to the
Einstein-Smoluchowski model for colloidal particles suspended in a fluid.
