Strong solutions of quasilinear integro-differential equations with singular kernels in several space dimensions

Electronic Journal of Differential Equations

关键词: Integro-differential equation;    strong solution;    singular kernel;    quasilinear.;   

DOI  :  

来源: DOAJ

【 摘 要 】

$$ u_t - a*A(u) = f,,$$ where $a$ is a scalar singular integral kernel that behaves like $t^{-alpha}$, $1/2 leq alpha < 1$ 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.

【 授权许可】

Unknown