Strong Solutions of Quasilinear Integro-Differential Equations with Singular Kernels in Several Space Dimensions
Southwest Texas State University, Department of Mathematics
For quasilinear integro-differential equations of the form ut − a ∗ A(u) = f , where a is a scalar singular integral kernel that behaves like t−α, 1 ≤ α < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.
Integro-differential equation, Strong solution, Singular kernel, Quasilinear
Engler, H. (1995). Strong solutions of quasilinear integro-differential equations with singular kernels in several space dimensions. <i>Electronic Journal of Differential Equations, 1995</i>(02), pp. 1-16.