A Geometrical Approach to the Study¶of Unbounded Solutions¶of Quasilinear Parabolic Equations

By Guy Barles, Samuel Biton, Olivier Ley. 2002

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/df4c56caddd09a4e0ce6023396b8334c2e651145

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Concentration in Lotka-Volterra Parabolic or Integral Equations: A General Convergence Result (2009, background): “1 in [4] (see also [11] for another proof of this claim).”
A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2009, background): “…adapted to obtain a spatial modulus of continuity, uniform in time (this is implemented in [22] for instance) Curiously, a modulus in time cannot be established so directly; it is known however that a “modulus of continuity in space” implies “modulus of continuity in time” (cf. Lemma 9.1 in [3]).”
Some homogenization results for non-coercive Hamilton–Jacobi equations (2006, methodology): “To do so, we use (a slight modification of) the approach used by Giga & Sato [21] for Hamilton-Jacobi Equations (see also Biton, Ley and the author [14] for the Mean Curvature Equation).”
On the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton–Jacobi equations (2009, unknown): “Moreover, if K δ := { y ∈ Ω : d ( y ) ≥ δ } for any δ > 0 , then, for all t ≥ η, the C 0 ,ν -norm of v ( · , t ) on K δ depends only on ν , δ , η , k f ∞ and the We postpone the proof of Proposition 3.1-(i) to the Appendix and refer the reader to [3, Lemma 9.1] for the proof of Proposition 3.1-(ii).”
A deterministic‐control‐based approach to fully nonlinear parabolic and elliptic equations (2010, background): “We note that while in [2, 24, 36] the level-set function U is just a tool for representing the solution, in our game-based interpretation it has a natural financial meaning.”