On the Cauchy problem for evolution -Laplace equation
Stanislav AntontsevUniversidade de Lisboa, Portugal
Sergey ShmarevUniversidad de Oviedo, Spain
We consider the Cauchy problem for the equation
with measurable but possibly discontinuous variable exponent . It is shown that for every and the problem has at least one weak solution , . We derive sufficient conditions for global boundedness of weak solutions and show that the bounded weak solution is unique.
Cite this article
Stanislav Antontsev, Sergey Shmarev, On the Cauchy problem for evolution -Laplace equation. Port. Math. 72 (2015), no. 2/3, pp. 125–144DOI 10.4171/PM/1961