Local existence and uniqueness of solutions to one-dimensional tumor invasion model
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In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) . And we show the local existence and uniqueness of solutions to approximate systems of the 1D modified tumor invasion model. Especially, we introduce a new function and show that our system is equivalent to the nonlinear second-order PDE, which should be reformulated by the new function. Roughly speaking, our system can be rewritten into only one second-order PDE and this fact is quite essential to show the local existence of solutions to the approximate systems.
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