Abstract
In this paper, the existence and uniqueness of local solutions to the initial and boundary value problem of a class of parabolic system related to the p-Laplacian are studied. The regularization method is used to construct a sequence of approximation solutions, with the help of monotone iteration technique, then we get the existence of solution of a regularized system. By the use of a standard limiting process, the existence of the local solutions of the system is obtained. Finally, the uniqueness of the solution is also proven.
Highlights
The objective of this paper is to study the existence and uniqueness of local solutions to the initial and boundary value problem of the parabolic system ( ) u= it − div ∇ui pi−2 ∇ui fi ( x, t, u1, u2, u3 ), ( x, t ) ∈ ΩT, (1.1)u= i ( x, 0) ui0 ( x), x ∈ Ω, (1.2)u= i ( x, t ) 0, ( x, t ) ∈ ∂Ω × (0,T ), (1.3)where pi > 2, i = 1, 2, 3, ΩT = Ω × (0,T ), Ω ⊂ Rn is a bounded domain with smooth boundary ∂Ω
The existence and uniqueness of local solutions to the initial and boundary value problem of a class of parabolic system related to the p-Laplacian are studied
System (1.1) is popular applied in non-Newtonian fluids [1] [2] and nonlinear filtration [3], etc
Summary
The existence and uniqueness of local solutions to the initial and boundary value problem of a class of parabolic system related to the p-Laplacian are studied. By the use of a standard limiting process, the existence of the local solutions of the system is obtained. The objective of this paper is to study the existence and uniqueness of local solutions to the initial and boundary value problem of the parabolic system
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