Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains
This work is devoted to some class of parabolic equations of high order with double nonlinearity which can be represented by a model equation ∂∂t(|u|k−2u)=∑α=1n(−1)mα−1∂mα∂xmαα[∣∣∣∂mαu∂xmαα∣∣∣pα−2∂mαu∂xmαα],m1,…,mn∈N,pn≥…≥p1>k,k>1. For the solution of the first mixed problem in a cylindric...
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Samara State Technical University
2013-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Online Access: | http://mi.mathnet.ru/eng/vsgtu1186 |
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doaj-8f8f802b7c8c4f789e03e459e6e6f7382020-11-25T01:41:18ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812013-03-011(30)828910.14498/vsgtu1186 Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains A. A. Leont'evL. M. KozhevnikovaThis work is devoted to some class of parabolic equations of high order with double nonlinearity which can be represented by a model equation ∂∂t(|u|k−2u)=∑α=1n(−1)mα−1∂mα∂xmαα[∣∣∣∂mαu∂xmαα∣∣∣pα−2∂mαu∂xmαα],m1,…,mn∈N,pn≥…≥p1>k,k>1. For the solution of the first mixed problem in a cylindrical domain D=(0,∞) ×Ω,Ω⊂Rn, n≥2, with homogeneous Dirichlet boundary condition and finite initial function the highest rate of decay established as t→∞. Earlier upper estimates were obtained by the authors for anisotropic equation of the second order and prove their accuracy.http://mi.mathnet.ru/eng/vsgtu1186 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. A. Leont'ev L. M. Kozhevnikova |
| spellingShingle |
A. A. Leont'ev L. M. Kozhevnikova Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| author_facet |
A. A. Leont'ev L. M. Kozhevnikova |
| author_sort |
A. A. Leont'ev |
| title |
Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| title_short |
Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| title_full |
Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| title_fullStr |
Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| title_full_unstemmed |
Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| title_sort |
solutions of anisotropic parabolic equations with double non-linearity in unbounded domains |
| publisher |
Samara State Technical University |
| series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| issn |
1991-8615 2310-7081 |
| publishDate |
2013-03-01 |
| description |
This work is devoted to some class of parabolic equations of high order with double nonlinearity which can be represented by a model equation
∂∂t(|u|k−2u)=∑α=1n(−1)mα−1∂mα∂xmαα[∣∣∣∂mαu∂xmαα∣∣∣pα−2∂mαu∂xmαα],m1,…,mn∈N,pn≥…≥p1>k,k>1.
For the solution of the first mixed problem in a cylindrical domain D=(0,∞) ×Ω,Ω⊂Rn, n≥2, with homogeneous Dirichlet boundary condition and finite initial function the highest rate of decay established as t→∞. Earlier upper estimates were obtained by the authors for anisotropic equation of the second order and prove their accuracy. |
| url |
http://mi.mathnet.ru/eng/vsgtu1186 |
| work_keys_str_mv |
AT aaleontev solutionsofanisotropicparabolicequationswithdoublenonlinearityinunboundeddomains AT lmkozhevnikova solutionsofanisotropicparabolicequationswithdoublenonlinearityinunboundeddomains |
| _version_ |
1725041539096248320 |