Part of the Applied Mathematical Sciences book series (AMS, volume 135)
A model that is not properly formulated mathematically cannot describe physical phenomena correctly.1 Our confidence that our equations, along with our boundary and initial conditions, can correspond with physical experience, is increased if their solutions satisfy the following three prerequisites:
the solutions must exist;
the solutions must be uniquely determined; and
the solutions must depend in a continuous fashion on the initial and boundary data.
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© Springer-Verlag Berlin Heidelberg 1999