Advanced search
Publication Cover
Complex Variables and Elliptic Equations
An International Journal
Volume 57, 2012 - Issue 11: Critical Point Theory and Elliptic Problems
Submit an article Journal homepage
471
Views
47
CrossRef citations to date
0
Altmetric
Original Articles

Monotone operator theory for unsteady problems in variable exponent spaces

L. Diening Mathematisches Institut, Ludwig-Maximilians Universität München, Theresienstr. 39, D-80333 Munich, Germany
,
P. Nägele Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104 Freiburg i. Br., Germany
&
M. Růžička Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104 Freiburg i. Br., GermanyCorrespondence[email protected]
Pages 1209-1231 | Received 22 Dec 2010, Accepted 17 Jan 2011, Published online: 19 Sep 2011

Citations (47)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (6)

Benkouider Soufiane & Rahmoune Abita. (2023) Blow-up time analysis of parabolic equations with variable nonlinearities. Applicable Analysis 102:18, pages 5082-5102.
Read now
Tahir Boudjeriou. (2022) Global existence and blow-up of solutions for a parabolic equation involving the fractional p(x)-Laplacian. Applicable Analysis 101:8, pages 2903-2921.
Read now
S. Antontsev & S. Shmarev. (2019) Higher regularity of solutions of singular parabolic equations with variable nonlinearity. Applicable Analysis 98:1-2, pages 310-331.
Read now
A. Youssfi, E. Azroul & B. Lahmi. (2016) Nonlinear parabolic equations with nonstandard growth. Applicable Analysis 95:12, pages 2766-2778.
Read now
S. Antontsev & S. Shmarev. (2016) On the localization of solutions of doubly nonlinear parabolic equations with nonstandard growth in filtration theory. Applicable Analysis 95:10, pages 2162-2180.
Read now
Yongqiang Fu & Mingqi Xiang. (2016) Existence of solutions for parabolic equations of Kirchhoff type involving variable exponent. Applicable Analysis 95:3, pages 524-544.
Read now

Articles from other publishers (41)

Stanislav Antontsev, Ivan Kuznetsov & Sergey Shmarev. (2023) Global existence and regularity for a pseudo-parabolic equation with p(x,t)-Laplacian. Journal of Mathematical Analysis and Applications 526:1, pages 127202.
Crossref
Rakesh Arora & Sergey Shmarev. (2022) Existence and regularity results for a class of parabolic problems with double phase flux of variable growth. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 117:1.
Crossref
Boris Andreianov & El Houssaine Quenjel. (2022) On Numerical Approximation of Diffusion Problems Governed by Variable-Exponent Nonlinear Elliptic Operators. Vietnam Journal of Mathematics 51:1, pages 213-243.
Crossref
Alex KaltenbachAlex Kaltenbach. 2023. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents 245 296 .
Alex KaltenbachAlex Kaltenbach. 2023. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents 43 111 .
Alex KaltenbachAlex Kaltenbach. 2023. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents. Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents 1 14 .
Zhongqing Li. (2022) Renormalized Solutions to a Class of Noncoercive Parabolic Equations with Variable Exponents. Mediterranean Journal of Mathematics 19:6.
Crossref
Mikhail Surnachev. (2022) On the weak Harnack inequality for the parabolic p ( x )-Laplacian. Asymptotic Analysis 130:1-2, pages 127-165.
Crossref
Rakesh Arora & Sergey Shmarev. (2022) Double-phase parabolic equations with variable growth and nonlinear sources. Advances in Nonlinear Analysis 12:1, pages 304-335.
Crossref
Stanislas Ouaro, Noufou Rabo & Urbain Traoré. (2022) Numerical analysis of nonlinear parabolic problems with variable exponent and L^1 data. Cubo, pages 187-209.
Crossref
Sergey Shmarev, Jacson Simsen & Mariza Stefanello Simsen. (2022) Stability for Evolution Equations with Variable Growth. Mediterranean Journal of Mathematics 19:4.
Crossref
Hamza Alaa, Nour Eddine Alaa & Abderrahim Charkaoui. (2021) Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions. Journal of Elliptic and Parabolic Equations 7:2, pages 815-839.
Crossref
A. Kaltenbach & M. Růžička. (2021) Variable exponent Bochner–Lebesgue spaces with symmetric gradient structure. Journal of Mathematical Analysis and Applications 503:2, pages 125355.
Crossref
Karthik Adimurthi, Sun-Sig Byun & Jung-Tae Park. (2021) End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains. Calculus of Variations and Partial Differential Equations 60:4.
Crossref
Chao Zhang & Xia Zhang. (2020) Some further results on the nonlocal p -Laplacian type problems . Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151:3, pages 953-970.
Crossref
Claudianor O. Alves & Tahir Boudjeriou. (2020) Existence of solution for a class of heat equation involving the p(x) Laplacian with triple regime. Zeitschrift für angewandte Mathematik und Physik 72:1.
Crossref
Rakesh Arora & Sergey Shmarev. (2021) Strong solutions of evolution equations with p(x,t)-Laplacian: Existence, global higher integrability of the gradients and second-order regularity. Journal of Mathematical Analysis and Applications 493:1, pages 124506.
Crossref
Gurusamy Arumugam & Andre H. Erhardt. (2020) Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion. Electronic Journal of Differential Equations 2020:01-132, pages 123.
Crossref
Tahir Boudjeriou. (2020) On the diffusion p(x)-Laplacian with logarithmic nonlinearity. Journal of Elliptic and Parabolic Equations 6:2, pages 773-794.
Crossref
Gurusamy Arumugam & André H. Erhardt. (2020) Existence of weak solutions to a certain homogeneous parabolic Neumann problem involving variable exponents and cross-diffusion. Journal of Elliptic and Parabolic Equations 6:2, pages 685-709.
Crossref
Elhoussine Azroul & Farah Balaadich. (2019) Young measure theory for unsteady problems in Orlicz–Sobolev spaces. Rendiconti del Circolo Matematico di Palermo Series 2 69:3, pages 1265-1278.
Crossref
Dominic Breit & Prince Romeo Mensah. (2020) Space-time approximation of parabolic systems with variable growth. IMA Journal of Numerical Analysis 40:4, pages 2505-2552.
Crossref
Gurusamy Arumugam & Jagmohan Tyagi. (2020) Nonnegative solutions to reaction–diffusion system with cross‐diffusion and nonstandard growth conditions. Mathematical Methods in the Applied Sciences 43:10, pages 6576-6597.
Crossref
Huashui Zhan. (2020) On Solutions of a Parabolic Equation with Nonstandard Growth Condition. Journal of Function Spaces 2020, pages 1-10.
Crossref
YANG LIU. (2018) EXISTENCE AND BLOW-UP OF SOLUTIONS TO A PARABOLIC EQUATION WITH NONSTANDARD GROWTH CONDITIONS. Bulletin of the Australian Mathematical Society 99:2, pages 242-249.
Crossref
Sergey Shmarev, Jacson Simsen, Mariza Stefanello Simsen & Marcos Roberto T. Primo. (2018) Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces. Asymptotic Analysis 111:1, pages 43-68.
Crossref
Jihoon Ok. (2018) Regularity for parabolic equations with time dependent growth. Journal de Mathématiques Pures et Appliquées 120, pages 253-293.
Crossref
Stanislav Antontsev, Ivan Kuznetsov & Sergey Shmarev. (2018) Global higher regularity of solutions to singular p(x,t)-parabolic equations. Journal of Mathematical Analysis and Applications 466:1, pages 238-263.
Crossref
A. Abbatiello, F. Crispo & P. Maremonti. (2018) Electrorheological fluids: Ill posedness of uniqueness backward in time. Nonlinear Analysis 170, pages 47-69.
Crossref
Sarah Eckstein & Michael Růžička. (2018) On the Full Space-Time Discretization of the Generalized Stokes Equations: The Dirichlet Case. SIAM Journal on Numerical Analysis 56:4, pages 2234-2261.
Crossref
Sergey Shmarev. (2018) On the continuity of solutions of the nonhomogeneous evolution -Laplace equation . Nonlinear Analysis 167, pages 67-84.
Crossref
André Erhardt. (2017) The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth. Mathematics 5:4, pages 50.
Crossref
Andr? H. Erhardt. (2016) Compact embedding for p(x,?t)-Sobolev spaces and existence theory to parabolic equations with p(x,?t)-growth. Revista Matem?tica Complutense 30:1, pages 35-61.
Crossref
Guy Vallet & Aleksandra Zimmermann. (2016) The stochastic p(ω,t,x)-Laplace equation with cylindrical Wiener process. Journal of Mathematical Analysis and Applications 444:2, pages 1359-1371.
Crossref
Claudianor O. Alves, Sergey Shmarev, Jacson Simsen & Mariza S. Simsen. (2016) The Cauchy problem for a class of parabolic equations in weighted variable Sobolev spaces: Existence and asymptotic behavior. Journal of Mathematical Analysis and Applications 443:1, pages 265-294.
Crossref
Guy Vallet, Petra Wittbold & Aleksandra Zimmermann. (2015) On a stochastic evolution equation with random growth conditions. Stochastics and Partial Differential Equations: Analysis and Computations 4:2, pages 246-273.
Crossref
Sun-Sig Byun & Jihoon Ok. (2016) Nonlinear Parabolic Equations with Variable Exponent Growth in Nonsmooth Domains. SIAM Journal on Mathematical Analysis 48:5, pages 3148-3190.
Crossref
Matthias Liero, Thomas Koprucki, Axel Fischer, Reinhard Scholz & Annegret Glitzky. (2015) p-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devices. Zeitschrift für angewandte Mathematik und Physik 66:6, pages 2957-2977.
Crossref
Yu A Alkhutov & V V Zhikov. (2014) Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent. Sbornik: Mathematics 205:3, pages 307-318.
Crossref
???? ????????????? ???????Yuriy Alexandrovich Alkhutov, ??????? ?????????? ?????Vasilii Vasil'evich Zhikov. (2014) ??????? ????????????? ? ?????????????? ??????? ?????????????? ????????? ? ?????????? ???????? ????????????Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent. ?????????????? ??????? Matematicheskii Sbornik 205:3, pages 3-14.
Crossref
C. Bauzet, G. Vallet, P. Wittbold & A. Zimmermann. (2013) On a $$p(t,x)$$ p ( t , x ) -Laplace evolution equation with a stochastic force. Stochastic Partial Differential Equations: Analysis and Computations 1:3, pages 552-570.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.