Тип публикации: статья из журнала
Год издания: 2022
Идентификатор DOI: 10.1515/jiip-2019-0045
Аннотация: <jats:title>Abstract</jats:title> <jats:p>We establish the stabilization of the strong solution <jats:inline-formula id="j_jiip-2019-0045_ineq_9999"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>u</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="falsПоказать полностьюe">(</m:mo> <m:mi>t</m:mi> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jiip-2019-0045_eq_0172.png" /> <jats:tex-math>{(u(t,x),k(t))}</jats:tex-math> </jats:alternatives> </jats:inline-formula> to the inverse problem for a pseudoparabolic equation <jats:inline-formula id="j_jiip-2019-0045_ineq_9998"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mrow> <m:mi>η</m:mi> <m:mo></m:mo> <m:mi>M</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mi>t</m:mi> </m:msub> <m:mo>+</m:mo> <m:mrow> <m:mi>M</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mi>f</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jiip-2019-0045_eq_0173.png" /> <jats:tex-math>{(u+\eta Mu)_{t}+Mu+k(t)u=f}</jats:tex-math> </jats:alternatives> </jats:inline-formula> with an unknown coefficient <jats:inline-formula id="j_jiip-2019-0045_ineq_9997"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>k</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jiip-2019-0045_eq_0297.png" /> <jats:tex-math>{k(t)}</jats:tex-math> </jats:alternatives> </jats:inline-formula> to the solution <jats:inline-formula id="j_jiip-2019-0045_ineq_9996"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msup> <m:mi>u</m:mi> <m:mi mathvariant="normal">∞</m:mi> </m:msup> <m:mo>,</m:mo> <m:msup> <m:mi>k</m:mi> <m:mi mathvariant="normal">∞</m:mi> </m:msup> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jiip-2019-0045_eq_0179.png" /> <jats:tex-math>{(u
Журнал: Journal of Inverse and Ill-Posed Problems
Выпуск журнала: Т. 0
ISSN журнала: 09280219
Издатель: Brill Academic Publishers