Question
Let a be a constant ≠ -c. Find the solution u(x,t) of (4.1) in the quadrant
x > 0,1>0, for which
u=f(x),      ut = g(x)    for t =0, x > 0
ut=aux      for x=0,t > 0,
where f and g are of class C² for x>0 and vanish near x=0. (Hint: Use (4.5)).
Show that generally no solution exists when α = - c.
Lu = utt - c²uᵪᵪ =0,       (4.1)
u=F (x+ct)+G (x-ct).      (4.5)
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        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
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        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        2.02mstwenty4_siteHomeworkLibraryController.php#97
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        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • select * from `subjects` where `subjects`.`id` in (60)
        910μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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