Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...

We consider a nonautonomous impulsive Cauchy problem of parabolic type involving a nonlocal initial condition in a Banach space X, where the operators in linear part (possibly unbounded) depend on ...

Given that the terminal condition is of at most linear growth, it is well known that a Cauchy problem admits a unique classical solution when the coefficient multiplying the second derivative is also ...