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The (simplified) Backus' Problem (BP) consists in finding a harmonic function u on the domain exterior to the three dimensional unit sphere S, such that u tends to zero at infinity and the norm of the gradient of u takes prescribed values g on S[...]texto impreso
The main goal of this paper is to study the asymptotic expansion near the boundary of the large solutions of the equation -Delta u + lambda u(m) = f in Omega, where lambda > 0, m > 1, f is an element of c(Omega), f > = 0, and Omega is an open [...]texto impreso
We consider a mathematical model, posed by J.E. Scheinkman, simulating that an industrial project takes place into the environment without destroying it. We introduce a change of variable leading the formulation to a nonlinear evolution problem [...]texto impreso
Díaz Díaz, Jesús Ildefonso ; Díaz Díaz, Gregorio ; Otero Juez, Jesús | Amsterdam Elsevier Science 2000 | 2006-04We show the existence and uniqueness of a viscosity solution for an oblique nonlinear problem suggested by the study of the Backus problem on the determination of the external gravitational potential of the Earth from surface measurements of the[...]texto impreso
We study the existence and uniqueness of solutions of a nonlinear stochastic pde proposed by R. North and R. F. Cahalan in 1982 for the modeling of non-deterministic variability (as, for instance, the volcano actions) in the framework of energy [...]texto impreso
Díaz Díaz, Gregorio ; Díaz Díaz, Jesús Ildefonso | American Institute of Mathematical Sciences | 2015-04This paper deals with several qualitative properties of solutions of some stationary equations associated to the Monge-Ampere operator on the set of convex functions which are not necessarily understood in a strict sense. Mainly, we focus our at[...]texto impreso
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This paper deals with several qualitative properties of solutions of some stationary and parabolic equations associated to the Monge-Ampère operator. Mainly, we focus our attention in the occurrence of a free boundary (separating the region wher[...]texto impreso
We study the existence, the asymptotic behaviour near the parabolic boundary and the uniqueness of the solutions of nonlinear reaction-diffusion equations, which blow up on the parabolic boundary. We extend some results for elliptic problems giv[...]texto impreso
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In this note we estimate the maximal growth rate at the boundary of viscosity solutions to ???u + ?|u| m?1 u = f in ? (? > 0, m > 3).In fact, we prove that there is a unique explosive rate on the boundary for large solutions. A version of Liou[...]
