On a nonlinear heat equation with functional dependence |
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| Authors: | H Leszczyński |
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| Institution: | 1. Department of Mathematics and Statistics , University of Guelph , Guelph, ON, N1G 2W1, Canada;2. Department of Applied Mathematics , University of Waterloo , Waterloo, ON, N2L 3G1, Canada |
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| Abstract: | We reduce the Cauchy problem for a heat equation with the nonlinear right-hand side which depends on some functionals to an equivalent integral equation. Considering mainly Banach spaces of continuous, bounded and exponentially bounded functions, we give some natural sufficient conditions for the existence and uniqueness of solutions to these equations. We give a counterexample which shows that the Lipschitz condition is, in general, insufficient for the Cauchy problem with unbounded data and with functional dependence to guarantee an existence result |
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| Keywords: | Banach contraction principle integral equation Lipschitz condition |
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