Existence results for nonlinear pseudoparabolic problems

N. Seam , Guy Vallet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this paper, we are interested in nonlinear pseudoparabolic problems of type: f(t,x,∂tu)-Div[a(x,u,∂tu)∇u]- Div[b(x,u,∂tu)∇∂ut]=g.f is a nondecreasing continuous function with respect to its third argument, a is bounded and b is positive and bounded. The result of existence is proved thanks to a time discretization scheme. Then, we derive some applications to the equation of Barenblatt, a degenerate case and differential inclusions. Finally, some numerical illustrations are proposed. © 2011 Elsevier Ltd. All rights reserved.

Domaines: Equations aux dérivées partielles [math.AP]

N. Seam, Guy Vallet. Existence results for nonlinear pseudoparabolic problems. Nonlinear Analysis: Real World Applications, 2011, 12 (5), pp.2625-2639. ⟨10.1016/j.nonrwa.2011.03.010⟩. ⟨hal-00865034⟩