Existence of Solutions for the Evolution 𝑝(𝑥)-Laplacian Equation Not in Divergence Form
The existence of weak solutions is studied to the initial Dirichlet problem of the equation 𝑢𝑡=𝑢div(|∇𝑢|𝑝(𝑥)−2∇𝑢), with inf 𝑝(𝑥)>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak sol...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/835495 |
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| Summary: | The existence of weak solutions is studied to the initial Dirichlet problem
of the equation 𝑢𝑡=𝑢div(|∇𝑢|𝑝(𝑥)−2∇𝑢), with inf 𝑝(𝑥)>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. |
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| ISSN: | 1110-757X 1687-0042 |