Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution

Key Points

• The central aim is to explore existence and regularity of solutions to parabolic equations with superlinear gradient terms.
• Analyzed two scenarios: one with initial data in an Orlicz space, and another with Lebesgue space data.
• Investigated conditions for solutions based on the nature of the lower order superlinear term.
• Studied behaviors under specific smallness conditions for data in Lebesgue spaces.
• Established conditions under which solutions exist and are regular.
• Results align with findings in previous research on similar types of equations.