Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: L-theory
| Autor: | Alfredo Lorenzi, Hiroki Tanabe, Angelo Favini |
|---|---|
| Přispěvatelé: | Favini, Angelo, Lorenzi, Alfredo, Tanabe, Hiroki |
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Applied Mathematics 010102 general mathematics Degenerate energy levels Scalar (mathematics) Analysi Differential operator 01 natural sciences Robin boundary condition law.invention 010101 applied mathematics Combinatorics Invertible matrix Linear parabolic integro-differential equation law Direct problems of parabolic type for time depending operator coefficients in Banach space Existence and uniqueness of solution 0101 mathematics Scalar field Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 447:579-665 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2016.10.029 |
| Popis: | The aim of this paper consists in solving integrodifferential problem of type (1.1) – (1.2) that may degenerate both in space and time. More precisely, { M p ( t ) } t ∈ [ 0 , T ] is a family of multiplication operators related to a scalar function m ( t , x ) that may vanish, while { L p ( t ) } t ∈ [ 0 , T ] is the realization of a family of linear second-order differential operators, with smooth coefficients, { L ( t ) } t ∈ [ 0 , T ] , { L p ( t ) } being invertible for all t ∈ [ 0 , T ] . Moreover, { B p ( t , s ) } t , s ∈ [ 0 , T ] , s ≤ t is the realization of a family { B ( t , s ) } t ∈ [ 0 , T ] , s ≤ t of linear second-order differential operators with smooth coefficients. Finally, the scalar functions a and b are such that 1 / a and b / a are Holder-continuous with suitable Holder exponents. |
| Databáze: | OpenAIRE |
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