Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods

Optimal Control Problems Governed By The Phase-Field Transition System

Author(s): Costica MOROSANU

Pp: 107-184 (78)

DOI: 10.2174/978160805350611201010107

* (Excluding Mailing and Handling)

Abstract

Some types of boundary optimal control problems governed by the nonlinear phase-field transition system, are introduced and analyzed in this Chapter.

The aim of Section 3.1 is to prove (for later use) a priori estimates in L2([0, T];H2( )) for unknown u, ' in phase-field system, in the presence of following boundary conditions (see (30), (300) in Preface):....


Keywords: Nonlinear parabolic systems, free boundary problems for PDE, inverse problems, necessary conditions for optimality, duality, abstract approximation theory, methods of approximations based on necessary conditions, stability and convergence of numerical methods, computer science, analysis of algorithms, methods of gradient type, phase transitions, applications in engineering and industry.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 1022 and `b`.`banner_from_date` <= 1739834426 and `b`.`banner_to_date` >= 1739834426 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.47msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 1022
      • 3: 1739834426
      • 4: 1739834426
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='5b4a0c6d1fce0d5c39c28fbd19703fe5'
      250μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    13Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
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        PHPDEBUGBAR_STACK_DATA
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        path_info
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        status_code
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        status_text
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        format
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        request_query
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-17 23:20:27GET/chapter/33341121815