Global regularity and blowup for a class of non-Newtonian polytropic variation-inequality problem from investment-consumption problems

This paper studies variation-inequality problems with fourth order non-Newtonian polytropic operators. First, the test function of the weak solution is constructed by using the difference operator. Then global regularity of the weak solution is obtained by some difference transformation and inequality amplification techniques. The weak solution is transformed into a differential inequality of the energy function. It is proved that the weak solution will blow up in finite time. Then, the upper bound and the blowup rate estimate of the blow up are given by handling some differential inequalities.