The generalized theory of terawatt laser pulse interaction with a low-dense porous substance of light chemical elements including laser light absorption and energy transfer in a wide region of parameter variation is developed on the base of the model of laser-supported hydrothermal wave in a partially homogenized plasma. Laser light absorption, hydrodynamic motion, and electron thermal conductivity are implemented in the hydrodynamic code, according to the degree of laser-driven homogenization of the laser-produced plasma. The results of numerical simulations obtained by using the hydrodynamic code are presented. The features of laser-supported hydrothermal wave in both possible cases of a porous substance with a density smaller and larger than critical plasma density are discussed along with the comparison with the experiments. The results are addressed to the development of design of laser thermonuclear target as well as and powerful neutron and X-ray sources.