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Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities

Boumediene Abdellaoui, Eduardo Colorado, Ireneo Peral (2004)

Journal of the European Mathematical Society

In this work we study the problem u t div ( | x | 2 γ u ) = λ u α | x | 2 ( γ + 1 ) + f in Ω × ( 0 , T ) , u 0 in Ω × ( 0 , T ) , u = 0 on Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , Ω N ( N 2 ) is a bounded regular domain such that 0 Ω , λ > 0 , α > 0 , - < γ < ( N 2 ) / 2 , f and u 0 are positive functions such...

Existence and nonexistence results for reaction-diffusion equations in product of cones

Abdallah Hamidi, Gennady Laptev (2003)

Open Mathematics

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.

Existence and properties of the Green function for a class of degenerate parabolic equations.

José C. Fernandes, Bruno Franchi (1996)

Revista Matemática Iberoamericana

It is known that degenerate parabolic equations exhibit somehow different phenomena when we compare them with their elliptic counterparts. Thus, the problem of existence and properties of the Green function for degenerate parabolic boundary value problems is not completely solved, even after the contributions of [GN] and [GW4], in the sense that the existence problem is still open, even if the a priori estimates proved in [GN] will be crucial in our approach (...).

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