The heat equation and the shrinking
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This article concerns the Cauchy problem for the partial differential equation
∂1u(t, x) - α∂22u(t, x) = ƒ(t, x, ∂p2 u(μ(t) t, x), ∂q2 u(t, v(t)x)).
Here t and x are real variables, p and q are positive integers greater than 1, and the shrinking factors μ(t), v(t) are positive-valued functions such that their suprema are less than 1.
CitationKawagishi, M., & Yamanaka, T. (2003). The heat equation and the shrinking. Electronic Journal of Differential Equations, 2003(97), pp. 1-14.
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