Pablo Alvarez Caudevilla

Pablo Alvarez Caudevilla is an Associate Professor in the Mathematics Department at Carlos III University of Madrid (UC3M). His research focuses on partial differential equations and their applications, with specialization in nonlinear analysis and mathematical modeling. He leads the research group "Ecuaciones Diferenciales y Aplicaciones" (Differential Equations and Applications).

His primary research interests include:

• Partial Differential Equations
• Nonlinear Analysis
• Mathematical Physics
• Calculus of Variations
• Applied Mathematics
• Higher-Order Differential Equations

Dr. Alvarez Caudevilla's publication record demonstrates deep expertise in fourth-order equations including thin film equations and bi-Laplace equations. His work addresses critical questions about existence, regularity, asymptotic behavior, and singularity formation in nonlinear PDEs. He has made significant contributions to understanding blow-up phenomena, gradient behavior, and self-similar solutions across multiple equation types.

He has secured competitive research funding as principal investigator for projects including "Ecuaciones en derivadas parciales y sistemas de EDPs acopladas: Análisis y aplicaciones" (2020-2023) funded by AGENCIA ESTATAL DE INVESTIGACION and "Ecuaciones diferenciales de alto orden de tipo parabolico y eliptico" (2013-2015) funded by MINISTERIO DE ECONOMÍA, COMERCIO Y EMPRESA.

Dr. Alvarez Caudevilla maintains an extensive international research network with regular collaborations at institutions including Université Paris 7/Laboratoire Jacques-Louis Lions (France), University of Bath (UK), Kyoto Sangyo University (Japan), and University of Sydney (Australia). His research mobility includes numerous funded visits across Europe, Asia, and Australia focusing on advanced problems in differential equations.