Regularity of complexified hyperbolic equations with integral conditions

ABSTRACT

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions involving harmonic complex exponential weights. The paper establishes existence, uniqueness, and regularity of the solutions.

Keywords:

• Complexification
• elliptic operators
• hyperbolic equations
• non-local boundary conditions
• integral conditions

AMS SUBJECT CLASSIFICATIONS:

• 35L05
• 35L10

Acknowledgments

This work was supported in part by the Zhejiang University/University of Illinois at Urbana-Champaign Institute.

Disclosure statement

No potential conflict of interest was reported by the author(s).