𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Cauchy problem for ut=Δu+|∇u|q

✍ Scribed by Brian H. Gilding; Mohammed Guedda; Robert Kersner

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
219 KB
Volume
284
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained.

📜 SIMILAR VOLUMES

Decay of Mass for the Equation ut=Δu−a(x
Decay of Mass for the Equation ut=Δu−a(x) up |∇u|q
✍ Ross G Pinsky 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 189 KB

Consider the quasilinear Cauchy problem where a>0, p and q satisfy p 0 and q 1 or p>1 and q=0, and This paper proves that the above equation possesses a unique positive classical solution and then investigates whether or not ##lim t Ä R d u(x, t) dx=0. In particular, it is shown that if a is on th