Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators
The nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t) (0≤t≤T), v(0)=v(λ)+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/519814 |
| Summary: | The nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t) (0≤t≤T), v(0)=v(λ)+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β) of all Eα-β-valued continuous functions φ(t) on [0,T] satisfying a Hölder condition with a weight (t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established. |
|---|---|
| ISSN: | 2356-6140 1537-744X |