scholarly journals On the solvability of the boundary value problem without initial condition for Schrödinger systems in infinite cylinders

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Nguyen Manh Hung ◽  
Nguyen Thi Lien
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Condition ◽  
Schrödinger Systems

On solutions to the heat equation with the initial condition in the Orlicz—Slobodetskii space

2014 ◽  
Vol 144 (4) ◽  
pp. 787-807 ◽  
Author(s):  
Agnieszka Kałamajska ◽  
Mirosłav Krbec
Keyword(s):  
Sobolev Space ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Boundary Value ◽  
Orlicz Function ◽  
Initial Condition ◽  
Lipschitz Boundary

We study the boundary-value problem ũt = Δxũ(x,t), ũ(x, 0) = u(x), where x ∈ Ω, t ∈ (0,T), Ω ⊆ ℝn−1 is a bounded Lipschitz boundary domain, u belongs to a certain Orlicz–Slobodetskii space YR,R(Ω). Under certain assumptions on the Orlicz function R, we prove that the solution u belongs to the Orlicz–Sobolev space W1,R(Ω × (0,T)).

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