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- Title
The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth.
- Authors
Erhardt, André H.
- Abstract
In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation ∂tu - div a(x, t,∇u) + λ (|u| p(x,t)-2u) = 0 in ΩT, where λ≥0 and ∂tu denote the partial derivative of u with respect to the time variable t, while∇u denotes the one with respect to the space variable x. Moreover, the vector-field a(x, t, ·) satisfies certain nonstandard p(x, t)-growth and monotonicity conditions. In this manuscript, we establish the existence of a unique weak solution to the corresponding Dirichlet problem. Furthermore, we prove the stability of this solution, i.e., we show that two weak solutions with different initial values are controlled by these initial values.
- Subjects
PARABOLIC differential equations; TIME variable gravity; EXISTENCE theorems; DIRICHLET problem; RAYLEIGH quotient
- Publication
Mathematics (2227-7390), 2017, Vol 5, Issue 4, p50
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math5040050