## THERMAL SCIENCE

International Scientific Journal

### BIHARMONIC HEAT EQUATION WITH GRADIENT NON-LINEARITY ON LP SPACE

**ABSTRACT**

In this paper, we deal with the biharmonic heat equation with gradient non-linearity. Under the suitable condition of the initial datum, we show that the global unique existence of the mild solution. The main technique in the paper is to use Banach's fixed point theorem in combination with the Lp-Lq evaluation of biharmonic operator.

**KEYWORDS**

PAPER SUBMITTED: 2021-07-18

PAPER REVISED: 2021-07-25

PAPER ACCEPTED: 2021-07-28

PUBLISHED ONLINE: 2021-12-18

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