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On a degenerate parabolic equation from double phase convection
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DOI：10.1186/s13662-021-03659-4.png)
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Abstract
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The initial-boundary value problem of a degenerate parabolic equation arising from double phase convection is considered. Let a(x) and b(x) be the diffusion coefficients corresponding to the double phase respectively. In general, it is assumed that a(x) + b(x) > 0 , x is an element of (Omega) over bar and the boundary value condition should be imposed. In this paper, the condition a(x) + b(x) > 0, x is an element of (Omega) over bar is weakened, and sometimes the boundary value condition is not necessary. The existence of a weak solution u is proved by parabolically regularized method, and u(t) is an element of L-2(Q(T)) is shown. The stability of weak solutions is studied according to the different integrable conditions of a(x) and b(x). To ensure the well-posedness of weak solutions, the classical trace is generalized, and that the homogeneous boundary value condition can be replaced by a(x)b(x)vertical bar(x is an element of partial derivative Omega) = 0 is found for the first time.
Keywords:
Degenerate parabolic equation
Double phase convection
Boundary value condition
Trace
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