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Moving fronts in integro-parabolic reaction-advection-diffusion equations. (English) Zbl 1269.45008
Summary: We consider initial-boundary value problems for a class of singularly perturbed nonlinear integro-differential equations. In applications, they are referred to as nonlocal reaction-advection-diffusion equations, and their solutions have moving interior transition layers (fronts). We construct the asymptotics of such solutions with respect to a small parameter and estimate the accuracy of the asymptotics. To justify the asymptotics, we use the asymptotic differential inequality method.
MSC:
45K05Integro-partial differential equations
45G10Nonsingular nonlinear integral equations
45N05Abstract integral equations, integral equations in abstract spaces