Duhamels Principle And The Method Of Descent For The Wave Equation
Mathematics Project Topics
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In this project we present investigation of the linear wave equation with the unknown function u,rnsubject to prescribed initial and/or boundary data, where Δ is n-dimensional Laplacian. In 1d, the solution of IVP is rendered by first reducing it into lower order PDE and then appealing to the method of characteristics, while, for BVP the method of reflection is employed to yield the pertinent solution. In higher dimension, explicit solution of IVP is derived as based on the method of spherical mean and the method of descent. In the sequel, Duhamel’s principle is used to get the solution of non-homogeneous wave equation from the associated homogeneous wave equation
Subsurface Intelligence & Critical Mineral Exploration
Modern Geology projects now focus on Machine Learning in Mineral Targeting, Carbon Capture & Storage (CCS) Geologic Modeling, and Critical Mineral Systems (Lithium, REEs). If your research involves Hydrogeological Connectivity, Seismic Inversion, or Geotechnical Site Characterization, ensure your analysis follows the JORC or NI 43-101 reporting standards and utilizes robust 3D Subsurface Visualization and Geochemical Fingerprinting frameworks.
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