Linearization of novel nonlinear diffusion equations with the Hilbert kernel and their exact solutions | Zendy

Yoshimasa Matsuno | Zendy

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Linearization of novel nonlinear diffusion equations with the Hilbert kernel and their exact solutions

Author(s) -

Yoshimasa Matsuno

Publication year - 1991

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.529134

Subject(s) - mathematics , linearization , nonlinear system , kernel (algebra) , mathematical analysis , hilbert space , initial value problem , simultaneous equations , variable (mathematics) , diffusion , differential equation , physics , pure mathematics , quantum mechanics , thermodynamics

Two novel nonlinear diffusion equations with the Hilbert kernel are proposed. The equations can be linearized by introducing appropriate dependent variable transformations. The initial value problems for the proposed equations are then solved exactly through the linearization and explicit nonperiodic and periodic solutions are constructed. The properties of solutions are investigated in detail. It is found that the blow up of solutions occurs at a finite time for both the nonperiodic and periodic cases due to the breakdown of certain analytic conditions imposed on the dependent variables.

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