Brian H. Gilding Livres

This monograph stems from research initiated in 1987, with roots tracing back to the 1970s when both authors were working on their doctoral theses, aiming to generalize the foundational paper by Oleinik, Kalashnikov, and Chzhou on nonlinear degenerate diffusion. Brian, guided by Bert Peletier at the University of Sussex and later at Delft University of Technology, focused on extending the mathematics to include nonlinear convection. Meanwhile, Robert worked under Anatolii Kalashnikov at Lomonosov State University, generalizing the mathematics to incorporate nonlinear absorption. The authors first met at a conference in Rome in 1985 and reconnected in Madrid in 1987, where they were both guests at 'La Residencia.' During this visit, the closure of the University 'Complutense' due to student demonstrations left them to explore shared research interests. They decided to collaborate on the characterization of the finite speed of propagation phenomenon for nonlinear reaction-convection-diffusion equations. Brian had recently completed work on nonlinear diffusion-convection, while Robert had addressed nonlinear diffusion-absorption, leading them to combine their efforts on this broader topic.

This monograph stems from research initiated in 1987, with roots tracing back to the 1970s during our doctoral studies, where we aimed to generalize the classic work of Oleinik, Kalashnikov, and Chzhou on nonlinear degenerate diffusion. Brian, mentored by Bert Peletier at the University of Sussex and later at Delft University of Technology, focused on extending the mathematics to incorporate nonlinear convection. Meanwhile, Robert studied under Anatolii Kalashnikov at Lomonosov State University, working on generalizing the mathematics to include nonlinear absorption. Our paths first crossed at a conference in Rome in 1985, and we reunited in Madrid in 1987, where we were both guests at 'La Residencia' during a university closure due to student protests. This unexpected circumstance allowed us to explore a shared research interest: the characterization of finite speed of propagation in nonlinear reaction-convection-diffusion equations. Brian had recently completed work on nonlinear diffusion-convection, while Robert had addressed nonlinear diffusion-absorption. It was clear that combining our efforts on this broader topic was a natural progression.