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Cauchy problem for doubly singular parabolic equation with gradient source
Author(s) -
Shang Haifeng,
Sun Junling,
Deng Lihua
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500010
Subject(s) - mathematics , cauchy distribution , initial value problem , term (time) , cauchy problem , mathematical analysis , function (biology) , physics , quantum mechanics , evolutionary biology , biology
This paper examines the Cauchy problem for doubly singular parabolic equation with a source term depending solely on the gradient. We establish the local and global existence of solutions when initial data is merely a function inL l o c r ( R N )( r ≥ 1 ). Moreover, the uniform L ∞ ‐estimates and gradient estimates of solutions are obtained.