Problems for parabolic equations with variable exponents of nonlinearity and time delay

Abstract

The initial-boundary value problems for parabolic equations with variable exponents of nonlinearity and time depended delay are considered. Existence and uniqueness of solutions of these problems are proved.

Keywords:

• Nonlinear parabolic equation
• equation with time delay
• initial-boundary value problem
• anisotropic parabolic equation
• equation with variable exponents of nonlinearity

AMS Subject Classifications:

• 35K20
• 35K55
• 35B45
• 35R10

Acknowledgements

We want to thank the referees for a careful reading and their helpful suggestions.

Notes

No potential conflict of interest was reported by the authors.