The Cauchy problem for the Finsler heat equation
2020 ◽
Vol 13
(3)
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pp. 257-278
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Keyword(s):
AbstractLet H be a norm of {\mathbb{R}^{N}} and {H_{0}} the dual norm of H. Denote by {\Delta_{H}} the Finsler–Laplace operator defined by {\Delta_{H}u:=\operatorname{div}(H(\nabla u)\nabla_{\xi}H(\nabla u))}. In this paper we prove that the Finsler–Laplace operator {\Delta_{H}} acts as a linear operator to {H_{0}}-radially symmetric smooth functions. Furthermore, we obtain an optimal sufficient condition for the existence of the solution to the Cauchy problem for the Finsler heat equation\partial_{t}u=\Delta_{H}u,\quad x\in\mathbb{R}^{N},\,t>0,where {N\geq 1} and {\partial_{t}:=\frac{\partial}{\partial t}}.
1995 ◽
Vol 115
(1)
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pp. 166-172
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Keyword(s):
2000 ◽
Vol 7
(4)
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pp. 627-631
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Keyword(s):
Keyword(s):
1963 ◽
Vol 17
(83)
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pp. 257-257
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