Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation partial derivative(t)u= u partial derivative(xx)(2)u-(c-1)(par tial derivative(x)u)(2) is known in literature as a qualitative mathematica l model of some biological phenomena. Here this equation is derived as a mo del of the groundwater flow in a water-absorbing fissurized porous rock; th erefore, we refer to this equation as a filtration-absorption equation. A f amily of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numeri cal experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still f ar from the ultimate state: identical zero. An open problem caused by the n onuniqueness of the solution of the Cauchy problem is discussed.