I entered a large, strip mall parking area and was driving at the vastly reduced speed one would use in such a situation. My intention was to park my car to enter a store in the mall. I turned a corner to park on the side of the building (parking options were limited). As I entered a parking space (moving at the speed one would drive to do so; essentially INCREDIBLY slowly; moving forward into the space at almost 0 MPH and already applying the brake). Suddenly and with no warning, the car violently lurched forward at a vastly increased speed. I pressed down on the brake harder to try to stop the vehicle, but it propelled into and over the concrete curb stop and into the thick brick wall in front of me. There is considerable damage to the front end of my vehicle as a result. I was horrified at this dangerous situation. My safety was definitely at risk. I feel very fortunate that I wasn't seriously injured (and that no one, either a pedestrian or another driver, was involved in the accident). The airbags didn't deploy and I was of course, wearing my safety belt, which kept me from any severe injury. I do feel some physical injury effects this morning however (sore neck, shoulder, back; a slight headache). I'm not aware of any warning lamps, messages, etc. going off, but I must say everything happened very quickly. I've reported the accident to my insurance company & filed a claim. Given that the incident happened on the evening before the July 4th holiday, my insurance company