TY - JOUR
T1 - Uniqueness of the Solutions of u<sub>t</sub>=Δu<sup>m</sup> and u<sub>t</sub>=Δu<sup>m</sup>-u<sup>p</sup> with Initial Datum a Measure: the Fast Diffusion Case
JO - Journal of Partial Differential Equations
VL - 2
SP - 143
EP - 159
PY - 1994
DA - 1994/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5678.html
KW - Porous medium equation
KW - Cauchy problem
KW - initial datum a measure
KW - uniqueness
AB -  In this paper, we study the Cauchy problems u_t = Δu^m \quad u(x, 0) = μ and u_t = Δu^m - u^p \quad u(x, 0) = μ where p &gt; 0, m &gt; (1 - \frac{α}{n})^+ and μ is a finite Radon measure. We prove the uniqueness of solution and the existence of solution.