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:''u''<sub>''xx''</sub> + ''u''<sub>''yy''</sub> = ''f'' (**)
We decompose the ___domain '''R'''² into two overlapping subdomains H<sub>1</sub> = (<nowiki>− ∞,1]</nowiki> × '''R''' and H<sub>2</sub> = <nowiki>[0,+ ∞</nowiki>) × '''R'''. In each subdomain, we will be solving a BVP of the form:
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