Locate lost Grandfather!

My Grandfather was born in Wales, UK in 1907 and I can trace his history back from there. He disappeared in about 1936 when my Mother was three years old. I cannot find any information about him from then on. Just out of curiosity for myself and my siblings, we want to find out what happened to him and if he remarried and had more children. I have full name, first marriage certificate and last known address but have drawn a blank from then on and don't know where to look. Can anyone help?