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Cauchy problem of some doubly degenerate parabolic equations with initial datum a measure. (English) Zbl 1073.35130
The author studies the existence of nonnegative solutions of the Cauchy problem u t =·(|u m | p-2 u m )-u q in N ×(0,), u(·,0)=μ in N , where p>1, m>0, q>0 and μ is a nonnegative bounded Radon measure. The existence is proved provided m(p-1)+p/N>1 and q<m(p-1)+p/N. It is also shown that these conditions are essentially optimal. The existence proof is based on the approximation of μ by smooth functions.
35K65Parabolic equations of degenerate type
35R05PDEs with discontinuous coefficients or data
35K15Second order parabolic equations, initial value problems
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