The behavior of solutions of quasi-linear heat equations
Tadashi Kawanago · Osaka City University (Osaka City University) · 1990
Σ ^ l (^, u) Vi{x) — = 0 on W(Λ?, 0) = w0 in Ω . Here, Ω(ZR(N>1) is a bounded domain with smooth boundary 9Ω and v= (vi> > N) denotes the outward normal on 9Ω. We assume that a=a and set R=(0, oo). These equations arise in heat flow through solids. In this case, u(xy t) represents the temperature of a position x at a time t in a solid Ω. If Ω is isotropic, we can set a(x, u)=k(x, u) S ί (δ ί ; is the Kronecker's dela delta) and k(x, ύ)>0 represents the thermal conductivity of the substance, which generally depends on a position Λ G Ω and the temperature u (see [6].) When the thermal