We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...

Abstract: Problems involving the classical linear partial differential equations of mathematical physics can be reduced to algebraic ones of a very much simpler structure by replacing the ...

Abstract: The main purpose of this paper is to present a reasonably complete picture of the results of the first phase of some recent research on the properties of solutions of nonlinear functional ...

Cascading processes accompanied by mixed-order transitions are characteristic for a wide range of ecological, financial, earth, climate, and social systems. To better understand the mechanisms ...

Granted permanent U.S. residence, as demonstrated by the issuance of a permanent residence card, i.e., a "Green Card" Granted U.S. citizenship Granted status as a "protected person" under 8 U.S.C.