Abstract

This paper studies the properties of solutions for a nonlinear diffusion problem with a gradient nonlinearity. The problem is formulated as a partial differential equation with a nonlinear term that depends on both the solution and its gradient. The main results are: existence and uniqueness of weak solutions in suitable function spaces; regularity and positivity of solutions; asymptotic behavior of solutions as time goes to infinity; comparison principles and maximum principles for solutions. The proofs are based on variational methods, fixed point arguments, energy estimates, and comparison techniques. Some examples and applications are also given to illustrate the features of the problem.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 3
Year: 2023

DOI: 10.12732/ijam.v36i3.7

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