The stability of the solutions of an anisotropic diffusion equation

Li, Mingguang

doi:10.1007/s11005-018-1135-3

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…; for examples, one can refer to [20,28,29], etc. Recently, using some techniques of [18], the existence and uniqueness of weak solutions to the following equation: 6) had been studied in [30][31][32], where a(x) satisfies…”

Section: Introductionmentioning

confidence: 99%

On a weak solution matching up with the double degenerate parabolic equation

Weng

2019

Bound Value Probl

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The well-posedness of weak solutions to a double degenerate evolutionary p(x)-Laplacian equation u t = div(b(x, t) ∇A(u) p(x)-2 ∇A(u)), is studied. It is assumed that b(x, t)| (x,t)∈Ω×[0,T] > 0 but b(x, t)| (x,t)∈∂Ω×[0,T] = 0, A (s) = a(s) ≥ 0, and A(s) is a strictly monotone increasing function with A(0) = 0. A weak solution matching up with the double degenerate parabolic equation is introduced. The existence of weak solution is proved by a parabolically regularized method. The stability theorem of weak solutions is established independent of the boundary value condition. In particular, the initial value condition is satisfied in a wider generality.

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Section: Introductionmentioning

confidence: 99%

On a weak solution matching up with the double degenerate parabolic equation

Weng

2019

Bound Value Probl

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Existence and stability of the doubly nonlinear anisotropic parabolic equation

Zhan

Feng

2021

Journal of Mathematical Analysis and Applications

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On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

Weng

2021

J Inequal Appl

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We study the existence of weak solutions to a Newtonian fluid∼non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). $$ u t = div ( b ( x , t ) | ∇ A ( u ) | p ( x ) − 2 ∇ A ( u ) + α ( x , t ) ∇ A ( u ) ) + f ( u , x , t ) . We assume that $A'(s)=a(s)\geq 0$ A ′ ( s ) = a ( s ) ≥ 0 , $A(s)$ A ( s ) is a strictly increasing function, $A(0)=0$ A ( 0 ) = 0 , $b(x,t)\geq 0$ b ( x , t ) ≥ 0 , and $\alpha (x,t)\geq 0$ α ( x , t ) ≥ 0 . If $$ b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], $$ b ( x , t ) = α ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × [ 0 , T ] , then we prove the stability of weak solutions without the boundary value condition.

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The stability of the solutions of an anisotropic diffusion equation

Cited by 3 publications

References 32 publications

On a weak solution matching up with the double degenerate parabolic equation

On a weak solution matching up with the double degenerate parabolic equation

Existence and stability of the doubly nonlinear anisotropic parabolic equation

On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

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