Is the end of Internet Explorer closer than we think?

I have been using Google Chrome for the last month at work. It started out as a frustrated response to Internet Explorer crashing random tabs. Then it became an experiment since although it was much faster than IE there were some applications that did not play nicely with Chrome. Now that I have worked through the problems, it is my production browser. On the other hand I still use Internet Explorer at home since I do not have the crashing tab problem. Considering the size of the smartphone and tablet market, if Internet Explorer cannot decisively when the desktop market the end is drawing near.