Reaction-diffusion equations in a noncylindrical thin domain

Pullback Attractors for Nonclassical Diffusion Equations in Noncylindrical Domains

The existence and uniqueness of a variational solution are proved for the following nonautonomous nonclassical diffusion equation ut − εΔut − Δu f u g x, t , ε ∈ 0, 1 , in a noncylindrical domain with homogeneous Dirichlet boundary conditions, under the assumption that the spatial domains are bounded and increase with time. Moreover, the nonautonomous dynamical system generated by this class of...

Generalized reaction–diffusion equations

This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion-rate estimation. A quasi-interpolating wavelet algorithm is u...

Reaction-diffusion Equations

I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied a...

Schrödinger equations in noncylindrical domains: exact controllability

We consider an open bounded set Ω ⊂ Rn and a family {K(t)}t≥0 of orthogonal matrices of Rn. Set Ωt = {x ∈Rn; x = K(t)y, for all y ∈Ω}, whose boundary is Γt. We denote by ̂ Q the noncylindrical domain given by ̂ Q =⋃0<t<T{Ωt ×{t}}, with the regular lateral boundary ̂ ∑ = ⋃0<t<T{Γt × {t}}. In this paper we investigate the boundary exact controllability for the linear Schrödinger equation u′ − iΔu= f...

Reaction-Diffusion Equations and Learning