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"Tugas akhir ini membahas fungsi Hypergeometri sebagai solusi persamaan Gauss. Persamaan Gauss adalah persamaan differensial homogen linier berorde dua, dengan variabel komplek dan koefisien berupa fungsi. Fungsi Hypergeometri adalah solusi persamaan Gauss yang didapat dengan metoda Frobenius atau disebut pula metoda deret pangkat/kuasa. Ternyata fungsi Hypergeometri ini sangat penting dalam fisika matematika."

"Fungsi Ferrers Terasosiasi Dengan Fungsi Legendre merupakan solusi dari Persamaan . Diferensial Terasosiasi Dari Legendre. Persamaan Diferensial ini muncul dari Persamaan Laplace dalam sistira koordinat bola. Tugas Akhir ini membahas tentang asal mula munculnya Fungsi Ferrers Terasosiasi Dengan Fungsi Legendre, beberapa sifat penting yang dimilikinya, serta relasi rekursif dari fungsi tersebut. Lalu, diberikan juga contoh penggunaan Fungsi Ferrers Terasosiasi Dengan Fungsi Legendre dalam masalah fisika matematika, untuk menghitung potensial elektrik interior suatu konduktor berbentuk bola berongga."

"Examines ill-posed, initial-history boundary-value problems associated with systems of partial-integrodifferential equations arising in linear and nonlinear theories of mechanical viscoelasticity, rigid nonconducting material dielectrics, and heat conductors with memory. Variants of two differential inequalities, logarithmic convexity, and concavity are employed. Ideas based on energy arguments, Riemann invariants, and topological dynamics applied to evolution equations are also introduced.These concepts are discussed in an introductory chapter and applied there to initial boundary value problems of linear and nonlinear diffusion and elastodynamics. Subsequent chapters begin with an explanation of the underlying physical theories."

"This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis, asymptotic constructions of solutions, energy and dispersive estimates, and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. ​"

"Topics in fractional differential equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. ​​Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena, in particular the modeling of memory-dependent and complex media such as porous media. "

"The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain.From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them."

"Effective dynamics of stochastic partial differential equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations.The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension."