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Properties of generalized degenerate parabolic systems
Cited 1 time in
Web of Science
Cited 0 time in Scopus
- Authors
- Issue Date
- 2022-03
- Publisher
- WALTER DE GRUYTER GMBH
- Citation
- Advances in Nonlinear Analysis, Vol.11 No.1, pp.1048-1084
- Abstract
- In this article, we consider the parabolic system (u(i))(t) = del.(mU(m-1) A(del u(i), u(i), x, t) + B(u(i), x, t)), (1 <= i <= k) in the range of exponents > m n-2/n where the diffusion coefficient U depends on the components of the solution u = (u(1), ..., u(k)). Under suitable structure conditions on the vector fields A and B, we first showed the uniform L-infinity boundedness of the functionU for t >= tau > 0. We also proved the law of L-1 mass conservation and the local continuity of solution u. In the last result, all components of the solution u have the same modulus of continuity if the ratio between U and u(i), (1 <= i <= k), is uniformly bounded above and below.
- ISSN
- 2191-9496
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