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Volume 7, Issue 4
Correspondence Between Renormalized and Entropy Solutions to the Parabolic Initial-Boundary Value Problem Involving Variable Exponents and Measure Data

Mykola Ivanovich Yaremenko

DOI: 10.12150/jnma.2025.1461

J. Nonl. Mod. Anal., 7 (2025), pp. 1461-1481.

Published online: 2025-07

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  • Abstract

We study the initial-boundary value parabolic problem involving variable exponent under the generalized Leray-Lions conditions. We clarify the definitions of entropy and renormalized solutions to such parabolic problems, and we establish the equivalence between these definitions of entropy and renormalized solutions to the parabolic problems with the Leray-Lions operator and with measure data.

  • Keywords

Capacity, diffuse measure data, entropy solution, exponential Lebesgue space, parabolic equation, renormalized solution, soft measure, variable Laplacian.

  • AMS Subject Headings

35K20, 35K55, 35D99, 35J70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1461, author = {Yaremenko , Mykola Ivanovich}, title = {Correspondence Between Renormalized and Entropy Solutions to the Parabolic Initial-Boundary Value Problem Involving Variable Exponents and Measure Data}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1461--1481}, abstract = {

We study the initial-boundary value parabolic problem involving variable exponent under the generalized Leray-Lions conditions. We clarify the definitions of entropy and renormalized solutions to such parabolic problems, and we establish the equivalence between these definitions of entropy and renormalized solutions to the parabolic problems with the Leray-Lions operator and with measure data.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1461}, url = {http://global-sci.org/intro/article_detail/jnma/24246.html} }
TY - JOUR T1 - Correspondence Between Renormalized and Entropy Solutions to the Parabolic Initial-Boundary Value Problem Involving Variable Exponents and Measure Data AU - Yaremenko , Mykola Ivanovich JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 1461 EP - 1481 PY - 2025 DA - 2025/07 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1461 UR - https://global-sci.org/intro/article_detail/jnma/24246.html KW - Capacity, diffuse measure data, entropy solution, exponential Lebesgue space, parabolic equation, renormalized solution, soft measure, variable Laplacian. AB -

We study the initial-boundary value parabolic problem involving variable exponent under the generalized Leray-Lions conditions. We clarify the definitions of entropy and renormalized solutions to such parabolic problems, and we establish the equivalence between these definitions of entropy and renormalized solutions to the parabolic problems with the Leray-Lions operator and with measure data.

Yaremenko , Mykola Ivanovich. (2025). Correspondence Between Renormalized and Entropy Solutions to the Parabolic Initial-Boundary Value Problem Involving Variable Exponents and Measure Data. Journal of Nonlinear Modeling and Analysis. 7 (4). 1461-1481. doi:10.12150/jnma.2025.1461
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