Continuous dependence of solutions to a fourth order evolution equation

Year 2025, Volume: 43 Issue: 1, 234 - 240, 28.02.2025

Sema Bayraktar Emine Çelik , Şevket Gür

Abstract

We consider an initial-boundary value problem for a fourth-order nonlinear parabolic equation with constant coefficients. Our primary focus lies in establishing a priori estimates for the solution to this equation, with a particular emphasis on its continuous dependence on both the initial data and parameters. Using energy estimates, we establish the continuous dependency for both the solution and its gradient concerning the fourth-order nonlinear parabolic equation.

Keywords

Continuous Dependence, Energy Estimates, Fourth-Order Parabolic Equations, 2020 Mathematics Subject Classification, 35G20, 35G31, 35Q35, 35K25, 35K55

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