Existence and Uniqueness of Solution for a Parabolic-Hyperbolic Equation with Multiplicative Control and Nonlocal Boundary Conditions
摘要
We consider a parabolic-hyperbolic equation with multiplicative control and nonlocal boundary conditions. By using the Riesz biorthogonal basis, the problem is reduced to a sequence of one-dimensional problems with alternative representations of their solutions. Conditions guaranteeing the existence and uniqueness of the solution to the analyzed problem are established.