Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks |
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Authors: | Linghai Zhang |
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Institution: | Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA |
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Abstract: | The author is concerned with the existence and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks. Previous methods do not apply in solving these problems because there is no maximum principle or conservation laws available to the integral differential equations. He applies fixed point theorems to prove the existence of the traveling waves. Then, he makes use of linearization technique as well as eigenvalue functions to study the exponential stability of the waves. |
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Keywords: | 35K57 35Q80 92C20 |
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