The solution is warming up and then doing
dynamic stretching prior to your intense training. I am a big proponent of yoga after class, but
static stretching after training is very helpful also.
At my old school in DC, Luis Pantoja does an AWESOME dynamic stretching routine after warmup drills (
Jiujitsu Maryland Jiu Jitsu Virginia - Washington DC - Brazilian Jiu Jitsu - Thai Boxing - Capoeira for adults and children). We had so few injuries as a result. However, most schools are fucking clueless about this stuff, make you do wedding carries, shrimps, etc. that get you warm but not loose, which is what you need to avoid injuries. They'll often say "stretch before class... your responsibility," but that's dumb, because you are supposed to warm up, then do
dynamic stretching and then hit your high-intensity stuff. So stretching, then class warmups is less effective.
As far as backs are concerned, this is HUGE, because it will limit your hip mobility which is integral to jiu jitsu. I also had a back injury from about 2 months ago that is still really bothering me. I have never had back problems in my life, but came into class late... didn't warm up and then drilled with a 230 lbs. moron with no coordination and wrenched my lower back. Lower back injuries, hip injuries and hamstring injuries are all tied together. Actually they say that tight hamstrings and hips are often the reason for most back problems. Since you need to improve mobility through your hamstrings, hips and lower back, I think the goal is to do a really good dynamic stretching warmup for those areas before class.
I did a bunch of online research about this and found the following good resources (in order of quality)
7 Dynamic Stretches to Improve Your Hip Mobility | StrongLifts.com
Tricks Tutorials.com
T NATION | Joint-by-Joint Approach to Training
Hamstring Stretches for Warm-up and Lower Back Pain
Some Videos
(my personal favorite stretch for this)