3 papers
math.AP2025
Irregular double-phase evolution problem: existence and global regularity
Rakesh Arora, Sergey Shmarev
We investigate the homogeneous Dirichlet problem for the irregular double-phase evolution equation \[ u_t-\operatorname{div} \left( a(z)|\nabla u|^{p(z)-2} \nabla u + b(z)|\nabla u…
math.AP2021
Existence and regularity results for a class of parabolic problems with double phase flux of variable growth
Rakesh Arora, Sergey Shmarev
We study the homogeneous Dirichlet problem for the equation \[ u_t-\operatorname{div}\left((a(z)\vert \nabla u\vert ^{p(z)-2}+b(z)\vert \nabla u\vert ^{q(z)-2})\nabla u\right)=f\qu…
math.AP2021
Stability for evolution equations with variable growth
Sergey Shmarev, Jacson Simsen, Mariza Stefanello Simsen
We study the character of dependence on the data and the nonlinear structure of the equation for the solutions of the homogeneous Dirichlet problem for the evolution -Lapla…