Global existence results for coupled nonlinear parabolic equations with weighted coefficients
В данной работе рассматривается класс нелинейных взвешенных параболических систем,
описывающих связанную динамику двух взаимодействующих скалярных полей. Установлены
достаточные условия глобального существования слабых решений в соответствующих взве-
шенных пространствах Соболева с использованием энергетических оценок и интегральных
неравенств. Кроме того, разработана численная схема, основанная на методе расщепления
Писмана-Рэчфорда в сочетании с алгоритмом Томаса, позволяющая эффективно прибли-
жать решения. Предложенная вычислительная методика реализована и проиллюстрирована
на двух- и трёхмерных численных экспериментах, включая динамические поверхностные
графики и анимированные профили. Полученные результаты демонстрируют качественные
свойства глобального решения, подтверждают аналитические выводы и дают дополнительное
представление о взаимодействии нелинейной диффузии, весовой неоднородности и межкомпо-
нентной связи.
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