Conditions for instantaneous support shrinking and sharp estimates for the support of the solution of the Cauchy problem for a doubly non-linear parabolic equation with absorption

Journal Article · Wed Apr 30 00:00:00 EDT 2008 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2008V199N04ABEH003931; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21096793

Degtyarev, S P ^[1]

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1. Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Donetsk (Ukraine)

Instantaneous support shrinking is studied for a doubly non-linear degenerate parabolic equation in the case of slow diffusion when, in general, the Cauchy initial data are Radon measures. For a non-negative solution, a necessary and sufficient condition for instantaneous support shrinking is obtained in terms of the local behaviour of the mass of the initial data. In the same terms, estimates are obtained for the size of the support, that are sharp with respect to order. Bibliography: 24 titles.

• OSTI ID: 21096793
• Journal Information: Sbornik. Mathematics, Vol. 199, Issue 4; Other Information: DOI: 10.1070/SM2008v199n04ABEH003931; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CAUCHY PROBLEM
DIFFUSION
EQUATIONS
MASS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS