Teori Regularitas Maksimal dan Penerapannya pada Sistem Navier--Stokes--Korteweg
Keywords:
Regularitas Maksimal, Persamaan Diferensial, Analisis Fungsional, Semigrup Analitik, Solvabilitas LokalSynopsis
Buku ini membahas konsep dan penerapan teori regularitas maksimal dalam analisis persamaan diferensial parsial, khususnya pada sistem fluida mampat dengan efek kapilaritas. Pembahasan mencakup persamaan evolusi, operator linear tak terbatas, semigrup analitik, ruang UMD, keterbatasan-R, serta analisis resolven sebagai landasan untuk memahami regularitas solusi. Teori tersebut kemudian diterapkan pada sistem Navier–Stokes–Korteweg melalui analisis pada berbagai geometri domain, mulai dari ruang penuh hingga domain umum dengan kondisi batas gelincir. Buku ini juga menguraikan pembuktian regularitas maksimal sistem linear serta solvabilitas lokal sistem nonlinear menggunakan prinsip kontraksi. Disusun secara sistematis dengan landasan teoretis, pembuktian matematis, dan ilustrasi, buku ini menjadi referensi bagi mahasiswa dan peneliti yang mendalami analisis fungsional, persamaan diferensial parsial, dan pemodelan matematika fluida.
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October 2, 2026
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