On a Class of Parabolic Integro-Differential Equations
Copyright policy )On a Class of Parabolic Integro-Differential Equations
Existence and uniqueness results for the integro-differential equation u_1(x, t) - au_{xx} (x, t) = c(x, t)u(x, t) + \int^1_0 k(s, x)h(s, t, u(s, t)) ds + f(x, t)\\\ ((x,t) \in Q) subject to the boundary condition u(x,t) = \varphi (x,t)\\\ ((x, t) \in R) and, especially, for the linear case h(s,t,u) = u are given. To this end, this equation is written as operator equation in a suitable Hölder space. The main tools are the calculation of the spectral radius in the linear case, and fixed point principles in the nonlinear case.
parabolic boundary, Dirichlet boundary condition, one-dimensional heat operator, Hölder spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Parabolic equations and parabolic systems, Integro-partial differential equations, Fixed-point theorems, Special properties of functions of several variables, Hölder conditions, etc., parabolic integro-differential equations, multiplication operator, Integro-differential operators
parabolic boundary, Dirichlet boundary condition, one-dimensional heat operator, Hölder spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Parabolic equations and parabolic systems, Integro-partial differential equations, Fixed-point theorems, Special properties of functions of several variables, Hölder conditions, etc., parabolic integro-differential equations, multiplication operator, Integro-differential operators
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