Renormalized solutions for a class of nonlinear evolution problems

@article{Blanchard1998RenormalizedSF,
  title={Renormalized solutions for a class of nonlinear evolution problems},
  author={Dominique Blanchard and Hicham Redwane},
  journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  year={1998},
  volume={77},
  pages={117-151}
}

EXISTENCE RESULTS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS IN ORLICZ SPACES

An existence result of a renormalized solution for a class of non- linear parabolic equations in Orlicz spaces is proved. No growth assumption is made on the nonlinearities.

EXISTENCE OF A SOLUTION FOR A CLASS OF NONLINEAR PARABOLIC SYSTEMS

An existence result of a solution for a class of nonlinear parabolic systems is established. The data belong to L 1 and no growth assumption is made on the nonlinearities.

EXISTENCE OF A RENORMALIZED SOLUTIONS FOR NONLINEAR PARABOLIC SYSTEMS WITTE UNBOUNDED NONLINEARITIES

We prove an existence result for a class of nonlinear parabolic systems with three unbounded nonlinearit ies. Without assumptions on the growth of some nonlinear terms, we prove the existence of a

RENORMALIZED SOLUTIONS FOR A NON-UNIFORMLY PARABOLIC EQUATION

In this paper we prove the existence of nonnegative renormalized solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the

Existence of renormalized solutions of degenerate elliptic-parabolic problems

  • K. AmmarP. Wittbold
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2003
We consider a general class of degenerate elliptic-parabolic problems associated with the equation b(υ)t = div a(υ, Dυ) + f. Existence of renormalized solutions is established for general L1 data.

Existence of Solution for Nonlinear Elliptic Equations with Unbounded Coefficients and L1 Data

An existence result of a renormalized solution for a class of nonlinear elliptic equations is established. The diffusion functions 𝑎(𝑥,𝑢,∇𝑢) may not be in (𝐿1loc(Ω))𝑁 for a finite value of the

Nonlinear evolution equations with noncoercive lower order terms

This paper is devoted to study the existence of renormalized solutions of the parabolic Dirichlet equations of prototype: where and the exponents of nonlinearities are given functions. The main

Renormalized Solutions for Nonlinear Degenerate Elliptic Problems with L 1 Data

We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x, u, Vu) which is not controlled with respect to u and which is not uniformly coercive on the

A Nonlinear Parabolic Problems with Lower Order Terms and Measure Data

We prove the existence of a renormalized solution to the nonlinear parabolic equation and the second member is assumed to be in L^1(Q T )+ L^p' (0, T, W^-1,p'(\Omega) )

Strongly nonlinear parabolic inequality in orlicz spaces via a sequence of penalized equations

An existence result of a entropy unilateral solution for a class of strongly nonlinear parabolic equations in Orlicz spaces is proved. No growth assumption is made on the nonlinearities.
...

References

SHOWING 1-10 OF 10 REFERENCES

On the Cauchy problem for Boltzmann equations: global existence and weak stability

We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge

Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness

  • D. BlanchardF. Murat
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1997
In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem where the data f and u0 belong to L1(Ω × (0, T)) and L1 (Ω), and where the function a:(0, T) ×

Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms

The authors study the nonlinear elliptic equation (*) −div(a(x,u,Du))−div(Φ(u))+g(x,u)=f(x)in Ω with the boundary condition (∗∗) u=0 on ∂Ω, where Ω is a bounded open subset of RN,

A few results on a class of degenerate parabolic equations

L’acces aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions

Compact sets in the spaceLp(O,T; B)

SummaryA characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method,