Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

2021 ◽  
pp. 1-35
Author(s):  
Galina Bizhanova
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Small Parameter ◽  
Unique Solvability ◽  
Time Derivative ◽  
Holder Space ◽  
Hölder Space ◽  
Space Solution ◽  
Unperturbed Problem

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | Σ in the boundary condition, where ε > 0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

scholarly journals Solution to a parabolic equation with integral type boundary condition

1993 ◽  
Vol 16 (4) ◽  
pp. 775-781
Author(s):  
Ignacio Barradas ◽  
Salvador Perez-Esteva
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Continuous Dependence ◽  
Linear Parabolic Equation ◽  
Type Condition ◽  
Integral Type ◽  
Holder Space ◽  
Hölder Space ◽  
Type Boundary ◽  
Type Boundary Condition

In this paper we study the existence, and continuous dependence of the solutionϑ=ϑ(x,t)on a Hölder spaceH2+γ,1+γ/2(Q¯τ)(Q¯τ=[0,1]×[0,τ],   0<γ<1)of a linear parabolic equation, prescribingϑ(x,0)=f(x),ϑx(1,τ)=g(τ)the integral type condition∫0bϑ(x,τ)dx=E(τ).

scholarly journals Boundary layer study of a nonlinear parabolic equation with a small parameter

2021 ◽  
Author(s):  
qin xulong ◽  
xu zhao ◽  
wenshu zhou
Keyword(s):  
Boundary Layer ◽  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Nonlinear Parabolic Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic ◽  
Initial Boundary Value

This paper is concerned with the initial-boundary value problem for a nonlinear parabolic equation with a small parameter. The existence of a boundary layer as the parameter goes to zero is obtained together with the estimation on the thickness of the boundary layer. The main result extends an earlier work of Frid and Shelukhin (1999).

scholarly journals Well-posedness of boundary value problems for reverse parabolic equation with integral condition

2018 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problems ◽  
Parabolic Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
Holder Space ◽  
Hölder Space ◽  
Coercive Stability

AbstractReverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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