# On the theory of remediability

Banach Center Publications (2003)

- Volume: 63, Issue: 1, page 165-176
- ISSN: 0137-6934

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topHassan Emamirad. "On the theory of remediability." Banach Center Publications 63.1 (2003): 165-176. <http://eudml.org/doc/282310>.

@article{HassanEmamirad2003,

abstract = {Suppose $\{G₁(t)\}_\{t≥0\}$ and $\{G₂(t)\}_\{t≥0\}$ are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators for G₁(t) and G₂(t), when the above map is well defined for all ρ ∈ (X) and satisfies the properties of a uniformly bounded semigroup on (X). In this paper we study some properties of the space (X) and we prove that when $A_i$ generate a regularized semigroup for i = 1,2, then the operator Δ defined on ℒ(X) by Δρ = A₂ρ + ρA₁ generates a tensor product regularized semigroup. Finally, we give two examples of remedial operators in radiotherapy and chemotherapy in proliferation of cancer cells.},

author = {Hassan Emamirad},

journal = {Banach Center Publications},

keywords = {remedial operator; regularized semigroups; tensor product semigroup},

language = {eng},

number = {1},

pages = {165-176},

title = {On the theory of remediability},

url = {http://eudml.org/doc/282310},

volume = {63},

year = {2003},

}

TY - JOUR

AU - Hassan Emamirad

TI - On the theory of remediability

JO - Banach Center Publications

PY - 2003

VL - 63

IS - 1

SP - 165

EP - 176

AB - Suppose ${G₁(t)}_{t≥0}$ and ${G₂(t)}_{t≥0}$ are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators for G₁(t) and G₂(t), when the above map is well defined for all ρ ∈ (X) and satisfies the properties of a uniformly bounded semigroup on (X). In this paper we study some properties of the space (X) and we prove that when $A_i$ generate a regularized semigroup for i = 1,2, then the operator Δ defined on ℒ(X) by Δρ = A₂ρ + ρA₁ generates a tensor product regularized semigroup. Finally, we give two examples of remedial operators in radiotherapy and chemotherapy in proliferation of cancer cells.

LA - eng

KW - remedial operator; regularized semigroups; tensor product semigroup

UR - http://eudml.org/doc/282310

ER -

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