Graham H. Williams

The exponential stability of the problem of transmission of the wave equation

The problem of exponential stability of the problem of transmission of the wave equation with lower-order terms is considered. Making use of the classical energy method and multiplier technique, we prove that this problem of transmission is exponentially stable.

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in

Evolving gene frequencies in a population with three possible alleles at a locus

{\mathbb R^{3}}

EXACT NEUMANN BOUNDARY CONTROLLABILITY FOR PROBLEMS OF TRANSMISSION OF THE WAVE EQUATION

and

Existence, uniqueness, and regularity for functions of least gradient

{\mathbb R^4}

Nonclassical symmetry solutions for reaction-diffusion equations with explicit spatial dependence

evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.