Professor Hassan Allouba

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Welcome to my page. I'm an associate professor in the Mathematical Sciences department at Kent State University.

I work mostly at the interface of PDEs, probability, and analysis. One focus of my research is the wellposedness (existense, uniqueness, and regularity) of 2 classes of PDEs/Stochastic PDEs (SPDEs) which I label as the two sides of the Brownian-time coin (after my work on the Brownian-time processes and its utility to view these two classes in a unified framework):

1. Time-fractional or high order PDEs/Stochastic PDEs (SPDEs) with memory; and
2. Kuramoto-Sivashinsky and related equations.

This includes my recent–and ongoing–formulation, solution and analysis of the sharp dimension-dependent regularity behavior of:

• the Kuramoto-Sivashinsky/Kuramoto-Sivashinsky Burgers PDE/SPDE in spatial dimensions d≥1 via my Brownina-time framework and its generalizations;
• the time fractional Burgers PDE/SPDE in spatial dimensions d≥1 via my Brownina-time framework and its generalizations;
• other related PDEs and SPDEs (including fractional, high order with memory, and Kuramoto-Sivashinsky type equations).

Education:

• Ph.D. - Cornell University - Center for Applied Mathematics
• M.S. - North Carolina State University - Operations Research
• B.S. - North Carolina State University - Electrical Engineering