RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



CMFD:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


CMFD, 2016, Volume 62, Pages 140–151 (Mi cmfd314)  

Coercive solvability of nonlocal boundary-value problems for parabolic equations

L. E. Rossovskii, A. R. Khanalyev

Department of Applied Math., RUDN University, 6 Miklukho-Maklaya st., 117198 Moscow, Russia

Abstract: In a Banach space $E$ we consider nonlocal problem
\begin{align*} &v'(t)+A(t)v(t)=f(t)\quad(0\leq t\leq1),
&v(0)=v(\lambda)+\mu\quad(0<\lambda\leq1) \end{align*}
for abstract parabolic equation with linear unbounded strongly positive operator $A(t)$ with independent of $t$, everywhere dense in $E$ domain $D=D(A(t))$. This operator generates analytic semigroup $\exp\{-sA(t)\}$ ($s\geq0$).
We prove the coercive solvability of the problem in the Banach space $C_0^{\alpha,\alpha}([0,1],E)$ $(0<\alpha<1)$ with the weight $(t+\tau)^\alpha$. This result was previously known only for a constant operator. We consider applications in the class of parabolic functional differential equations with transformation of spatial variables and in the class of parabolic equations with nonlocal conditions on the boundary of domain. Thus, this describes parabolic equations with nonlocal conditions both in time and in spatial variables.

Full text: PDF file (202 kB)
References: PDF file   HTML file
UDC: 517.95+517.98

Citation: L. E. Rossovskii, A. R. Khanalyev, “Coercive solvability of nonlocal boundary-value problems for parabolic equations”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 62, PFUR, M., 2016, 140–151

Citation in format AMSBIB
\Bibitem{RosHan16}
\by L.~E.~Rossovskii, A.~R.~Khanalyev
\paper Coercive solvability of nonlocal boundary-value problems for parabolic equations
\inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia)
\serial CMFD
\yr 2016
\vol 62
\pages 140--151
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd314}


Linking options:
  • http://mi.mathnet.ru/eng/cmfd314
  • http://mi.mathnet.ru/eng/cmfd/v62/p140

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Современная математика. Фундаментальные направления
    Number of views:
    This page:200
    Full text:54
    References:22

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020