In this paper, we prove the existence of non-negative solutions for a non-local third order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann type operator (which can be defined using the periodic Hilbert transform). The main difficulties are due to the fact that this equation is non-local, and that the natural energy estimates are not as good as in the case of the thin film equation.ou
The aim of this paper is to study the solvability of solutions of non-local problems with integral c...
In the present paper we study the local behavior of non-negative weak solutions of a wide class of d...
We consider a free-boundary problem for a class of fourth-order nonlinear parabolic equations which ...
In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for α ∈ (0, 2). The ...
of solutions for a third order non-local equation appearing in crack dynamics C. Imbert∗and A. Melle...
This paper deals with a nonlinear degenerate parabolic equation of order α between 2 and 4 which is ...
AbstractIn this paper, we deal with a class of non-classical parabolic equations which arise from so...
AbstractThe existence of local (in time) solutions of the initial–boundary value problem for the fol...
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear...
In the paper a non local problem for a model parabolic hyperbolic equation is researched. The third ...
Karch G, Kaßmann M, Krupski M. A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Jour...
We prove global existence of a nonnegative weak solution to a degenerate parabolic system, which mod...
In this article, we provide existence results for a general class of nonlocal and nonlinear second-o...
We recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimens...
AbstractIn this paper, we investigate the blowup properties of the positive solutions to the followi...
The aim of this paper is to study the solvability of solutions of non-local problems with integral c...
In the present paper we study the local behavior of non-negative weak solutions of a wide class of d...
We consider a free-boundary problem for a class of fourth-order nonlinear parabolic equations which ...
In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for α ∈ (0, 2). The ...
of solutions for a third order non-local equation appearing in crack dynamics C. Imbert∗and A. Melle...
This paper deals with a nonlinear degenerate parabolic equation of order α between 2 and 4 which is ...
AbstractIn this paper, we deal with a class of non-classical parabolic equations which arise from so...
AbstractThe existence of local (in time) solutions of the initial–boundary value problem for the fol...
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear...
In the paper a non local problem for a model parabolic hyperbolic equation is researched. The third ...
Karch G, Kaßmann M, Krupski M. A Framework for Nonlocal, Nonlinear Initial Value Problems. SIAM Jour...
We prove global existence of a nonnegative weak solution to a degenerate parabolic system, which mod...
In this article, we provide existence results for a general class of nonlocal and nonlinear second-o...
We recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimens...
AbstractIn this paper, we investigate the blowup properties of the positive solutions to the followi...
The aim of this paper is to study the solvability of solutions of non-local problems with integral c...
In the present paper we study the local behavior of non-negative weak solutions of a wide class of d...
We consider a free-boundary problem for a class of fourth-order nonlinear parabolic equations which ...