The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth
Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, Oslo 0316, Norway
Academic Editor: Michel Chipot
Received: 17 September 2017 / Revised: 5 October 2017 / Accepted: 8 October 2017 / Published: 12 October 2017
In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation
denote the partial derivative of u
with respect to the time variable t
denotes the one with respect to the space variable x
. Moreover, the vector-field
satisfies certain nonstandard
-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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Erhardt, A.H. The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth. Mathematics 2017, 5, 50.
Erhardt AH. The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth. Mathematics. 2017; 5(4):50.
Erhardt, André H. 2017. "The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth." Mathematics 5, no. 4: 50.
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