Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
2016 ◽
Vol 23
(3)
◽
pp. 303-321
◽
Keyword(s):
AbstractWe study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form${\partial b(x,u)\over\partial t}-\operatorname{div}(a(x,t,u,\nabla u))+g(x,t,u% ,\nabla u)+H(x,t,\nabla u)=\mu\quad\text{in }\Omega\times(0,T),$where the right-hand side belongs to ${L^{1}(Q_{T})+L^{p^{\prime}}(0,T;W^{-1,p^{\prime}}(\Omega))}$ and ${b(x,u)}$ is unbounded function of u, ${{-}\operatorname{div}(a(x,t,u,\nabla u))}$ is a Leray–Lions type operator with growth ${|\nabla u|^{p-1}}$ in ${\nabla u}$. The critical growth condition on g is with respect to ${\nabla u}$ and there is no growth condition with respect to u, while the function ${H(x,t,\nabla u)}$ grows as ${|\nabla u|^{p-1}}$.
2019 ◽
Vol 5
(1)
◽
pp. 1-21
◽
2019 ◽
Vol 38
(6)
◽
pp. 99-126
2011 ◽
Vol 09
(02)
◽
pp. 161-186
◽
2015 ◽
Vol 1
(1)
◽
pp. 201-214
◽
1971 ◽
Vol 7
(1)
◽
pp. 147-155
◽
2009 ◽
Vol 139
(2)
◽
pp. 381-392
◽
2011 ◽
Vol 192
(2)
◽
pp. 273-296
◽
Keyword(s):
2007 ◽
Vol 187
(4)
◽
pp. 563-604
◽