Global boundary null-controllability of one-dimensional semilinear heat equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586683" target="_blank" >RIV/67985840:_____/24:00586683 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/dcdss.2024003" target="_blank" >https://doi.org/10.3934/dcdss.2024003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdss.2024003" target="_blank" >10.3934/dcdss.2024003</a>
Alternative languages
Result language
angličtina
Original language name
Global boundary null-controllability of one-dimensional semilinear heat equations
Original language description
This paper addresses the boundary null-controllability of the semilinear heat equation ∂ty - ∂xxy + f(y) = 0, (x, t) ∈ (0, 1) × (0, T). Assuming that the function f ∈ C1(R) satisfies lim sup|r|→+∞ |f(r)|/(|r| ln3/2 |r|) ≤ β for some β > 0 small enough and that the initial datum belongs to L∞(0, 1), we prove the global null-controllability using the Schauder fixed point theorem and a linearization for which the term f(y) is seen as a right side of the equation. Then, assuming that f satisfies lim sup|r|→∞ |f'(r)|/ ln3/2 |r| ≤ β for some β small enough, we show that the fixed point application is contracting yielding a constructive method to approximate boundary controls for the semilinear equation. The crucial technical point is a regularity property of a state-control pair for a linear heat equation with L2 right hand side obtained by using a global Carleman estimate with boundary observation. Numerical experiments illustrate the results. The arguments developed can notably be extended to the multi-dimensional case.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical systems - Series S
ISSN
1937-1632
e-ISSN
1937-1179
Volume of the periodical
17
Issue of the periodical within the volume
7
Country of publishing house
US - UNITED STATES
Number of pages
47
Pages from-to
2251-2297
UT code for WoS article
001150177100001
EID of the result in the Scopus database
2-s2.0-85195043592