Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains
Larisa Mikhailovna Kozhevnikova, Алексей Александрович Леонтьев · Ufimskii Matematicheskii Zhurnal · 2013
This work is devoted to a class of parabolic equations with a double nonlinearity whose representative is a model equationFor the solution of Dirichlet initial boundary value problem in a cylindrical domain 𝐷 = (0, ∞) ×Ω, Ω ⊂ R 𝑛 , 𝑛 ≥ 2, with homogeneous Dirichlet boundary condition and compactly supported initial function, precise estimates the decay rate as 𝑡 → ∞ are established.Earlier these results were obtained by the authors for 𝑘 ≥ 2. The case 𝑘 ∈ (1, 2) differs by the method of constructing Galerkin approximations that for an isotropic model equation was proposed by E.R. Andriyanova and F.Kh. Mukminov.