Exact(60)
and (13) has a unique weak solution.
Then (1.1) has a unique weak solution.
Step 1. Problem (1.1) has a globally unique weak solution.
admits a unique weak solution in W 0 1, p.
We prove that has a unique weak subsequential limit in.
Then, there exists a unique weak solution of (1.1).
A full-discrete finite element scheme to approximate the unique weak solution is designed.
Convergence of the numerical method to the unique weak solution with bounded total variation is proved.
The direct problem is shown to have a unique weak solution by studying its variational formulation.
We prove that { x n } has a unique weak subsequential limit in F ( T ).
From Definition 2.8 this is also the unique weak solution to system (1.2).
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