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 - <p style="text-align: justify;">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.</p>