Nonlinear parabolic equations with nonstandard growth

Abstract

In this paper, we study the solvability of the initial-boundary value problem for second-order nonlinear parabolic equations with nonstandard growth conditions and -source terms. In the model case, these equations include the p-Laplacian with a variable exponent p(x, t). We prove that if the variable exponent p is bounded away from both 1 and and is log-Hölder continuous, then the problem has a weak solution which satisfies the energy equality.

Keywords:

• Nonlinear parabolic equations
• variable exponents
• weak solutions

AMS Subject Classifications:

• 35K55
• 46E35
• 35D30

Acknowledgements

We would like to thank the referees for proofreading the manuscript and providing suggestions and comments that improved the paper.

Notes

No potential conflict of interest was reported by the authors.