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Full-Text Articles in Applied Mathematics
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker
Electronic Theses and Dissertations
Modeling our atmosphere and determining forecasts using numerical methods has been a challenge since the early 20th Century. Most models use a complex dynamical system of equations that prove difficult to solve by hand as they are chaotic by nature. When computer systems became more widely adopted and available, approximating the solution of these equations, numerically, became easier as computational power increased. This advancement in computing has caused numerous weather models to be created and implemented across the world. However a challenge of approximating these solutions accurately still exists as each model have varying set of equations and variables to …
Convolution Inequalities And Applications To Partial Differential Equations., Matthew Reynolds
Convolution Inequalities And Applications To Partial Differential Equations., Matthew Reynolds
Electronic Theses and Dissertations
In this dissertation we develop methods for obtaining the existence of mild solutions to certain partial differential equations with initial data in weighted L p spaces and apply them to some examples as well as improve the solutions to some known PDEs studied extensively in the literature. We begin by obtaining a version of a Stein-Weiss integral inequality which we will use to obtain general convolution inequalities in weighted L p spaces using the techniques of interpolation. We will then use these convolution inequalities to make estimates on PDEs that will help us obtain mild solutions as fixed points of …