Abstract:The article considers a parabolic-type boundary value problem with a divergent principal part, when the boundary condition contains the time derivative of the required function:
{ ut−d/dxiai(x,t,u,∇u)+a(x,t,u,∇u)=0,a0ut+ai(x,t,u,∇u)cos(v,xi)=g(x,t,u,),(x,t)∈St, u(x,0)= u0(x), x∈Ω
Such nonclassical problems with boundary conditions containing the time derivative of the desired function arise in the study of a number of applied problems, for example, when the surface of a body, whose temperature is the same at… Show more
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