J. Nonl. Evol. Equ. Appl. 2020 (5), pp. 65-93, published on September 23, 2020:

Nonlinear Parabolic Problem With Variable Exponent And Measure Data

S. Ouaro, U. Traore

Laboratoire de Mathématique et Informatique (LAMI), UFR, Sciences Exactes et Appliquées, Université de Ouagadougou, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso

Received on September 19, 2018, revised version on July 9, 2019
Accepted on October 8, 2019

Communicated by Alexander Pankov

Abstract.  In this paper we prove the existence and uniqueness of renormalized solution to nonlinear parabolic equations with variable exponent and measure data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.
Keywords:Parabolic equation, variable exponent, parabolic capacity, measures.
2010 Mathematics Subject Classification:   35J20, 35J25, 35D30, 35B38, 35J60.

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