Interpolation of nonlinear partial differential operators and generation of differentiale evolutions |
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Authors: | Eric Schechter |
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Institution: | Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37235 USA |
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Abstract: | By interpolating between Sobolev spaces we find that many partial differential operators become continuous when restricted to a sufficiently small domain. Hence some techniques from the theory of ordinary differential equations can be applied to some p.d.e.'s. Using these ideas, we study a class of nonlinear evolutions in a Banach space. We obtain some very simple existence and continuous dependence results. The theory is applicable to reaction-diffusion equations, dispersion equations, and hyperbolic equations before shocks develop. |
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