Instituto de Matemática e Computação
Universidade Federal de Itajubá
37500-903 Itajubá, Minas Gerais, Brazil
email: jacson@unifei.edu.br
Jacson Simsen
Abstract:
We extend the results in Kloeden-Simsen [CPAA 2014] to
\(p(x,t)\)-Laplacian problems on time-dependent Lebesgue spaces with
variable exponents. We study the equation
$$\displaylines{
\frac{\partial u_\lambda}{\partial t}(t)-\operatorname{div}\big(D_\lambda(t,x)|\nabla
u_\lambda(t)|^{p(x,t)-2}\nabla u_\lambda(t)\big)
+|u_\lambda(t)|^{p(x,t)-2}u_\lambda(t)
=B(t,u_\lambda(t))
}$$
on a bounded smooth domain \(\Omega\) in \(\mathbb{R}^n\),
\(n\geq 1\), with a homogeneous Neumann boundary condition, where the
exponent \(p(\cdot)\in C(\bar{\Omega}\times [\tau,T],\mathbb{R}^+)\) satisfies
\(\min p(x,t)>2\), and \(\lambda\in [0,\infty)\) is a parameter.
Submitted February 18, 2023. Published July 24, 2023.
Math Subject Classifications: 35K55, 35K92, 35A16, 35B40, 35B41, 37B55.
Key Words: Non-autonomous parabolic problems; variable exponents; p-Laplacian; pullback attractors; upper semicontinuity.
DOI: https://doi.org/10.58997/ejde.2023.50
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Jacson Simsen Instituto de Matemática e Computação Universidade Federal de Itajubá 37500-903 Itajubá, Minas Gerais, Brazil email: jacson@unifei.edu.br |
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