Publication: The one-dimensional nonlinear heat-equation with absorption: regularity of solutions and interfaces
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1987-01
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Society for Industrial and Applied Mathematics
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We consider the equation ut=(Um)xx-λun with m>1, λ>0, n≥m as a model for heat diffusion with absorption. Hence we assume that u≥0 for xЄR, t≥0. We study the regularity of the solution to the Cauchy problem for this degenerate parabolic equation. When the initial datum uo(X)is positive only in a part of the space R, we also study the regularity of the free boundaries that appear. The asymptotic behavior of solutions and free boundaries is also discussed.
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