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4 papers · 2 filters
An infinity Laplace equation with gradient term and mixed boundary conditions
Scott N. Armstrong, Charles K. Smart, Stephanie J. Somersille
We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation \[ -Δ_\infty u - β|Du| = f, \] subject to Dirichlet or mixed Dirichl…
Optimal lower bounds on the local stress inside random thermoelastic composites
Yue Chen, Robert Lipton
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomec…
Long-time asymptotics for fully nonlinear homogeneous parabolic equations
Scott N. Armstrong, Maxim Trokhimtchouk
We study the long-time asymptotics of solutions of the uniformly parabolic equation \[ u_t + F(D^2u) = 0 \quad {in} \R^n\times \R_+, \] for a positively homogeneous operator , s…
On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning
Burak Aksoylu, Horst R. Beyer
We consider the diffusion equation in the setting of operator theory. In particular, we study the characterization of the limit of the diffusion operator for diffusivities approach…