Generic well-posedness of an inverse parabolic problem - the Hölder-space approach

1996 ◽  
Vol 12 (3) ◽  
pp. 195-205 ◽  
Author(s):  
Mourad Choulli ◽  
Masahiro Yamamoto
Keyword(s):  
Parabolic Problem ◽  
Well Posedness ◽  
Holder Space ◽  
Hölder Space ◽  
Inverse Parabolic Problem ◽  
Space Approach

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.

Maximal Regularity for Fractional Cauchy Equation in Hölder Space and Its Approximation

2019 ◽  
Vol 19 (4) ◽  
pp. 779-796 ◽  
Author(s):  
Li Liu ◽  
Zhenbin Fan ◽  
Gang Li ◽  
Sergey Piskarev
Keyword(s):  
Cauchy Problem ◽  
Maximal Regularity ◽  
Well Posedness ◽  
Cauchy Equation ◽  
Holder Space ◽  
Hölder Space ◽  
Implicit Difference Schemes ◽  
Existence And Stability ◽  
Fractional Cauchy Problem ◽  
Resolvent Families

AbstractWe derive the well-posedness and maximal regularity of the fractional Cauchy problem in Hölder space {C_{0}^{\gamma}(E)}. We also obtain the existence and stability of new implicit difference schemes for the general approximation to the nonhomogeneous fractional Cauchy problem. Our analysis is based on the approaches of the theory of β-resolvent families, functional analysis and numerical analysis.

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 A Note on the Parabolic Differential and Difference Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Yasar Sozen ◽  
Pavel E. Sobolevskii
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Difference Scheme ◽  
Positive Operator ◽  
Difference Equations ◽  
Well Posedness ◽  
Holder Space ◽  
Strongly Positive Operator ◽  
Ill Posed ◽  
General Banach Space

The differential equationu'(t)+Au(t)=f(t)(−∞<t<∞)in a general Banach spaceEwith the strongly positive operatorAis ill-posed in the Banach spaceC(E)=C(ℝ,E)with norm‖ϕ‖C(E)=sup−∞<t<∞‖ϕ(t)‖E. In the present paper, the well-posedness of this equation in the Hölder spaceCα(E)=Cα(ℝ,E)with norm‖ϕ‖Cα(E)=sup−∞<t<∞‖ϕ(t)‖E+sup−∞<t<t+s<∞(‖ϕ(t+s)−ϕ(t)‖E/sα),0<α<1, is established. The almost coercivity inequality for solutions of the Rothe difference scheme inC(ℝτ,E)spaces is proved. The well-posedness of this difference scheme inCα(ℝτ,E)spaces is obtained.

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