In this article the flows of perfect gas behind converging and divergi
ng strong shock waves under isothermal condition in the cases of spher
ical and cylindrical symmetry are examined. A diverging shock wave is
formed by energy supply according to a power law. These waves propagat
e in a uniform medium at rest and all conservation laws hold at the fr
onts of these shock waves. It was established that in the case of conv
erging waves for any value of the ratios of specific heats gamma is an
element of (1,3) the solution of the problem under consideration exis
ts and is unique. When gamma greater than or equal to 3 the problem ha
s more than one solution. In the case of diverging shock waves the sol
ution exists and is unique for any gamma from the interval gamma is an
element of (1,5/3] and any value of power in the energy input law.