Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Shmarev, Sergey"'
Autor:
Arora, Rakesh, Shmarev, Sergey
We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equations of $p(x,t)$-Laplace type %with nonlinear sources depending on the so
Externí odkaz:
http://arxiv.org/abs/2407.20133
Autor:
Arora, Rakesh, Shmarev, Sergey
We consider the homogeneous Dirichlet problem for the parabolic equation \[ u_t- \operatorname{div} \left(|\nabla u|^{p(x,t)-2} \nabla u\right)= f(x,t) + F(x,t, u, \nabla u) \] in the cylinder $Q_T:=\Omega\times (0,T)$, where $\Omega\subset \mathbb{R
Externí odkaz:
http://arxiv.org/abs/2305.10877
Autor:
Arora Rakesh, Shmarev Sergey
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 25-60 (2024)
We consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,
Externí odkaz:
https://doaj.org/article/ebbc10516e3747b6887433cdfcbe00e9
Autor:
Arora, Rakesh, Shmarev, Sergey
We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation \[ u_t-\sum_{i=1}^ND_{x_i}\left(|D_{x_i}u|^{p_i(x,t)-2}D_{x_i}u\right)=f(x,t) \] in the cylinder $\Omega\times (0,T)$, where $\Omega\subset \mathbb{R}^N$, $N\geq 2$,
Externí odkaz:
http://arxiv.org/abs/2208.07723
Publikováno v:
In Nonlinear Analysis: Real World Applications December 2024 80
Autor:
Arora, Rakesh, Shmarev, Sergey
We study the homogeneous Dirichlet problem for the equation \[ u_t-\operatorname{div}\left((a(z)\vert \nabla u\vert ^{p(z)-2}+b(z)\vert \nabla u\vert ^{q(z)-2})\nabla u\right)=f\quad \text{in $Q_T=\Omega\times (0,T)$}, \] where $\Omega\subset \mathbb
Externí odkaz:
http://arxiv.org/abs/2109.03597
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 $p(x,t)$-Laplacian with the nonlinear source \[ u_t-\Delta_{p(x,t)}u=f(x,t,u),\quad
Externí odkaz:
http://arxiv.org/abs/2103.13476
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 February 2024 530(1)
Autor:
Arora, Rakesh, Shmarev, Sergey
This paper addresses the questions of existence and uniqueness of strong solutions to the homogeneous Dirichlet problem for the double phase equation with operators of variable growth: \[ u_t - div \left(|\nabla u|^{p(z)-2} \nabla u+ a(z) |\nabla u|^
Externí odkaz:
http://arxiv.org/abs/2010.08306
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