Comparison principles for systems of impulsive parabolic equations
For classical solutions of weakly coupled fully nonlinear parabolic differential equations \(u^{k}_{t} = f^{k}(t,x,u,\nabla u^{k}, \nabla^{2} u^{k}) (x \in Q \subset \mathbb R^{n}, 0 < t < T)\) with various boundary conditions and impulsive perturbations \(u^{k}(t_{i},\cdot) - u^{k}(t_{i}-0,\cdot) = g^{k}(\cdot, u^{k}(t_{i} - 0,\cdot)), 0 < t_{1} < t_{2}< \cdots,\) various weak and strong comparison results are proved, if the system is elliptic and quasimonotonicity holds for the \(f^{k}\) and \(g^{k}\) with respect to the \(u\)-arguments.
scientific article; zbMATH DE number 1000266