Maximal Solutions of Singular Diffusion Equations with General Initial Data
In the range −1 < m ≤ 0 the Cauchy problem admits infinitely many solutions if for instance U o is nonnegative and integrable. We show existence and uniqueness of a maximal solution of the problem for initial data U o ∈ M+(R), the set of nontrivial, nonnegative and locally bounded Borel measures. These solutions are characterized in terms of a suitable decay rate as |x| → ∞ (good solutions). Since we also show that every good solution defined in a strip Q T possesses a uniquely defined trace in M+(R) at t = 0, a complete theory of maximal solutions for our equation is obtained.
KeywordsInitial Data Cauchy Problem Borel Measure Harnack Inequality Maximal Solution
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