OPTIMAL EXISTENCE AND UNIQUENESS IN A NONLINEAR DIFFUSION-ABSORPTION EQUATION WITH CRITICAL EXPONENTS

Authors
CHAVES M VAZQUEZ JL WALIAS M
Citation
M. Chaves et al., OPTIMAL EXISTENCE AND UNIQUENESS IN A NONLINEAR DIFFUSION-ABSORPTION EQUATION WITH CRITICAL EXPONENTS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 127, 1997, pp. 217-242
Citations number
20
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
127
Year of publication
1997
Part
2
Pages
217 - 242
Database
ISI
SICI code
0308-2105(1997)127:<217:OEAUIA>2.0.ZU;2-4
Abstract
We study the existence and uniqueness of non-negative solutions of the nonlinear parabolic equation u(t) = Delta(u(m)) - u(m), m > 1, posed in Q = R-N X (0, infinity) With general initial data u(x, 0)= u(0)(x) greater than or equal to 0. We find optimal exponential growth conditi ons for existence of solutions. Similar conditions apply for uniquenes s, but the growth rate is different. Such conditions strongly depart f rom the linear case In = 1, u(t) = Delta u - u, and also from the pure ly diffusive case u(t) = Delta u(m).