The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources”

Cauchy problem for semilinear parabolic equations with initial data in H (R) spaces.

Francis Ribaud (1998)

Revista Matemática Iberoamericana

Similarity:

We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂U - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces H (R). In most of the studies on this subject, the initial data U(x) belongs to Lebesgue spaces L(R) or to supercritical fractional Sobolev spaces H (R) (s > n/p). Our purpose is to study the intermediate cases (namely for 0 < s < n/p). We give some mapping properties for functions with polynomial...

Non-negative solutions of generalized porous medium equations.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1986)

Revista Matemática Iberoamericana

Similarity:

The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations ∂u/∂t = Δφ(u),  x ∈ Rn, 0 < t < T ≤ +∞  (1.1) Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these...

Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

Daniele Andreucci, Marianne K. Korten (1993)

Revista Matemática Iberoamericana

Similarity:

The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1 loc (Rn x (0,T)) to (0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)), for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection...

Weak solutions for a well-posed Hele-Shaw problem

S. N. Antontsev, A. M. Meirmanov, V. V. Yurinsky (2004)

Bollettino dell'Unione Matematica Italiana

Similarity:

We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in B ⁢ V spaces, prove a comparison theorem, and show that the solution depends continuously on...