Displaying 181 – 200 of 269

Showing per page

Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano, Noriko Mizoguchi (1996)

Banach Center Publications

In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if ( t , x ) R + × Ω u = 0 if ( t , x ) R + × Ω , where Ω R N is a bounded domain with smooth boundary ∂Ω and g : R + × Ω ¯ × R R is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.

Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities

Y. Akdim, J. Bennouna, M. Mekkour, H. Redwane (2012)

Applicationes Mathematicae

We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), b ( x , u ) | t = 0 = b ( x , u ) in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in L ¹ ( Q ) + L p ' ( 0 , T ; W - 1 , p ' ( Ω ) ) and b(x,u₀) ∈ L¹(Ω).

Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (1999)

Annales Polonici Mathematici

We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.

Existence of solutions for a model of self-gravitating particles with external potential

Andrzej Raczyński (2004)

Banach Center Publications

We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.

existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium

Cristelle Barillon, Georgy M. Makhviladze, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types of solutions are found: classical, critical and multivalued. Regularity of solutions is studied as well as their behavior depending on the size of the domain and on the coefficient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.

Currently displaying 181 – 200 of 269