Existence and Uniqueness of a Renormalized Solution for a Fairly General Class of Nonlinear Parabolic Problems

@article{Blanchard2001ExistenceAU,
  title={Existence and Uniqueness of a Renormalized Solution for a Fairly General Class of Nonlinear Parabolic Problems},
  author={Dominique Blanchard and François Murat and Hicham Redwane},
  journal={Journal of Differential Equations},
  year={2001},
  volume={177},
  pages={331-374}
}

Existence and uniqueness of renormalized solution for nonlinear parabolic equations in Musielak Orlicz spaces

This paper is devoted to the study of a class of parabolic equation of type$$ \frac{\partial u}{\partial t} -div(A(x,t,u,\nabla u) +B(x,t,u)) =f \quad\mbox{in}\quad Q_T, $$where $div(A(x,t,u,\nabla

Renormalized solutions for stochastic $p$-Laplace equations with $L^1$-initial data: The multiplicative case

We consider a p-Laplace evolution problem with multiplicative noise on a bounded domain D ⊂ R with homogeneous Dirichlet boundary conditions for 1 < p < ∞. The random initial data is merely

Weak-renormalized solutions for three species competition model in ecology

TLDR
The existence of weak-renormalized solutions of the three species degenerate predator–prey model is investigated and it is assumed that there is no growth condition on the nonlinearities.

Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

We consider a general class of parabolic equations of the type with Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized

Nonlinear elliptic and parabolic equations with measure data

Well-posedness of renormalized solutions for a stochastic p -Laplace equation with L^1 -initial data

We consider a $p$-Laplace evolution problem with stochastic forcing on a bounded domain $D\subset\mathbb{R}^d$ with homogeneous Dirichlet boundary conditions for $1<p<\infty$. The additive noise term

Volumes finis et solutions renormalisées, applications à des systèmes couplés.

On s’interesse dans cette these a montrer que la solution approchee, par la methode des volumes finis, converge vers la solution renormalisee de problemes elliptiques ou paraboliques a donnee L1.

Renormalized solutions for the fractional p(x)-Laplacian equation with L^1 data

In this paper, we prove the existence and uniqueness of nonnegative renormalized solutions for the fractional p(x)-Laplacian problem with L1 data. Our results are new even in the constant exponent

EXISTENCE RESULT FOR NONLINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

In this paper, we prove, the existence of a renormalized solution for a class of nonlinear parabolic problems whose prototype is where QT = Ω × (0, T), Ω is an open and bounded subset of ℝN, N ≥ 2, T
...

References

SHOWING 1-10 OF 18 REFERENCES

Resultats d'existence et comportement asymptotique pour des equations paraboliques quasi-lineaires

On etudie, dans un ouvert borne, des equations paraboliques associees a des operateurs de type leray-lions. On donne tout d'abord un theoreme d'existence, s'il existe une sous solution inferieure a

PARTIAL DIFFERENTIAL EQUATIONS

Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear

On the existence of weak solutions for quasilinear parabolic initial-boundary value problems

Synopsis Structure conditions on a strongly nonlinear operator A(u) are given, under whichthe initial-Dirichlet-boundary value problem for has weak solutions.

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) ×

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

Nonlinear Parabolic Equations with Measure Data

In this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model isu′−div(|∇u|p−2∇u)=μonΩ×(0,T), (P)with homogeneous Cauchy–Dirichlet boundary

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,