Analyzing the nonlinear heat transfer equation by AGM

Null Controllability of a Nonlinear Heat Equation

Radiative heat transfer in nonlinear Kerr media

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We obtain a fluctuation-dissipation theorem describing thermal electromagnetic fluctuation effects in nonlinear med...

Spectral Properties of Stationary Solutions of the Nonlinear Heat Equation

(1.1)  ut −∆u = |u|u, u|∂Ω = 0, u(0) = u0. It is well known that the above initial value problem is locally well-posed. More precisely, there exists a maximal time 0 < Tu0 ≤ ∞ and a (unique) function u ∈ C([0, Tu0), C0(Ω))∩C((0, Tu0), C(Ω))∩C((0, Tu0), C0(Ω)) which is a classical solution of (1.1) on (0, Tu0) and such that u(0) = u0. Furthermore, there is the blowup alternative: either Tu0 ...

The Nonlinear Heat Equation on W -Random Graphs

For systems of coupled differential equations on a sequence of W -random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medve...

On the Exact Controllability of a Nonlinear Stochastic Heat Equation

The bounded open subsetG of Rn is assumed to have a smooth boundary and g is continuous from L2(0,T ;L2(G)) into L2(0,T ;L2(G)). The existence of a solution of the linear version of (1.1) is established in Section 3 of the paper. The nonlinear case is considered in Section 4. The main assumptions of the paper and some preliminary results are given in Section 2. Exact controllability of the wave...