On 4 January 2026, the Nguyen Van Cu Campus of the VNUHCM–University of Science (HCMUS) hosted the institutional-level doctoral thesis defence of researcher Trần Quang Minh. Specialising in Mathematical Analysis (Class of 2022), Trần Quang Minh completed his doctoral research under the scientific supervision of Associate Professor Lý Kim Hà. Entitled “Applications of Nonlinear Analysis to the Study of Certain Partial Differential Equations”, the thesis investigates the Hadamard well-posedness of several classes of nonlinear partial differential equations (PDEs) and systems. The research rigorously clarifies fundamental mathematical properties, including the existence, uniqueness, and continuous dependence of solutions on initial data, while offering a detailed analysis of solution behaviour.

To address complex mathematical problems, the candidate systematically employed advanced tools from modern nonlinear analysis, including fixed-point theorems, monotone operator theory, and compactness methods. The mathematical models examined in the thesis arise from a range of applied sciences—such as physics, classical mechanics, and biology—highlighting the close interaction between abstract mathematical theory and practical application.

The research outcomes are synthesised from one manuscript and three peer-reviewed articles published in leading international journals, including Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, and Nonlinear Analysis: Real World Applications.

The thesis is structured around three principal strands. The first focuses on nonlinear pseudo-parabolic systems, investigating existence, uniqueness, global behaviour, decay estimates, and finite-time blow-up phenomena. The second concerns nonlinear Navier–Lamé systems, analysing Hadamard well-posedness and specific solution properties. The third examines fourth-order nonlinear dispersive wave equations, with particular emphasis on equations containing exponential growth terms.

Collectively, these results make a significant contribution to the theory of nonlinear partial differential equations and extend the scope of nonlinear analytical methods in contemporary mathematics.

Beyond its current achievements, the thesis proposes several advanced directions for future research, including the study of global compact attractors and their finite dimensionality, as well as the incorporation of stochastic terms into existing models. These directions hold strong potential for both theoretical development and applied relevance.

Following the defence, the Board Representative announced the Resolution, confirming that the thesis meets the highest scientific standards. In recognition of its originality and scholarly quality, the Examination Board unanimously recommended the conferment of the degree of Doctor of Mathematics upon Trần Quang Minh.