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"This clearly written, self-contained volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated? The topics treated include the study of the Boltzmann collision operator, the study of the initial-value problem for the Boltzmann equation with "small" and "near equilibrium" data, global smooth solvability of the initial-value problem for the Vlasov-Poisson system with smooth initial data of unrestricted size, conditions under which the initial-value problem for the Vlasov-Maxwell system has global-in-time solutions (in both the smooth and weak senses), and more."

"The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p>2 or m>1) and in the singular range (1"

"Aktivitas transportasi merupakan salah satu penyumbang biaya terbesar terhadap biaya logistik, terutama di wilayah perkotaan. Sedangkan, permasalahan transportasi barang di wilayah perkotaan terus bertambah kompleks, seiring dengan bertumbuhnya jumlah pelanggan yang didukung oleh pertumbuhan transaksi e-commerce dan pertumbuhan jumlah warung atau yang lebih dikenal dengan nama nanostores. Salah satu permasalahan yang disebabkan oleh meningkatnya jumlah pelanggan ini adalah masalah penentuan rute distribusi. Dengan meningkatnya jumlah titik pengiriman, kombinasi rute yang mungkin dihasilkan juga meningkat dengan eksponensial yang secara langsung berpengaruh terhadap kompleksitas perhitungan dalam mendapatkan rute yang optimal. Permasalahan pemilihan rute ini sendiri dikenal dengan nama Vehicle Routing Problem (VRP). Pada penelitian ini, peneliti akan berfokus pada penyelesaian varian paling dasar dari VRP, yaitu Capacitated Vehicle Routing Problem (CVRP) dengan jumlah pelanggan di atas 1.000 titik pengiriman (berskala sangat besar). Output utama dari penelitian ini adalah model optimasi CVRP berskala sangat besar dan output tambahan berupa rancangan rute yang dapat meminimalkan biaya pengiriman pada permasalahan perancangan rute distribusi di Indonesia dengan jumlah pelanggan mencapai 32.223 pelanggan.

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Transportation activity is one of the main cost-driver of overall logistics cost, especially in urban area. Whereas, the transportation problem in urban area is becoming more complex in response to the growth of customers number that fueled by the rapid growth of e-commerce and number of nanostores. One of the main problem that emerged from the growth of customers number is finding the optimal route for distribution. The possible routes combination is growing exponentially in respect to the increase of destination number, rising the complexity to obtain the optimal solution. This problem of finding the optimal routes combination is known in combinatorial optimization as Vehicle Routing Problem (VRP). In this paper, we will focus on the most basic variant of VRP called Capacitated Vehicle Routing Problem (CVRP) with the number of customers more than 1.000 (very large scale). The main output of this research is the optimization model for very large scale CVRP and the additional output is the optimal distribution route for a problem with 32.223 customers in Indonesia."