  We study a number of domain wall forming models where various types of defect
junctions can exist. These illustrate some of the mechanisms that will
determine the evolution of defect networks with junctions. Understanding these
mechanisms is vital for a proper assessment of a number of cosmological
scenarios: we will focus on the issue of whether or not cosmological frustrated
domain wall networks can exist at all, but our results are also relevant for
the dynamics of cosmic (super)strings, where junctions are expected to be
ubiquitous. We also define and discuss the properties that would make up the
ideal model in terms of hypothetical frustrated wall networks, and provide an
explicit construction for such a model. We carry out a number of numerical
simulations of the evolution of these networks, analyze and contrast their
results, and discuss their implications for our no-frustration conjecture.
