domain-wall (DW) networks are known to approach a relativistic scaling regime on fixed radiation- and matter-dominated backgrounds, forming the basis of the no-frustration conjecture. However, this picture assumes that the defect network remains gravitationally subdominant. We investigate the self-consistent evolution of DWs by coupling the velocity-dependent one-scale model to the Friedmann equation and radiation energy transfer. The resulting autonomous system allows the cosmic expansion history to evolve dynamically rather than being imposed externally. We demonstrate analytically that gravitational backreaction qualitatively changes the phase-space structure: the radiation-era scaling solution, which is a stable attractor on a fixed background, becomes a saddle once the expansion rate is promoted to a dynamical degree of freedom. Furthermore, we establish that no stable fixed point exists within the physical phase space. Consequently, the scaling regime survives only as a transient stage, and all trajectories are driven toward a wall dominated and kinematically frustrated state in which the walls freeze in comoving coordinates. Our results demonstrate that the scaling attractor is not preserved in self-gravitating DW networks and reveal the generic late-time frustration dynamics of wall domination.

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• Cosmic strings & domain walls
• Cosmology