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The Annals of Statistics, ISSN 0090-5364, 10/2010, Volume 38, Issue 5, pp. 2916 - 2957
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2014, Volume 163, Issue 7, pp. 1405 - 1490
In this paper, we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X, d, m) which is stable under measured... 
MATHEMATICS | SOBOLEV SPACES | TRANSPORT | INEQUALITIES | STABILITY | COMPACT ALEXANDROV SPACES | FINSLER MANIFOLDS | WASSERSTEIN SPACES | HEAT-FLOW | GRADIENT FLOWS | GEOMETRY | 60J65 | 35K05
Journal Article
Journal of Physics: Conference Series, ISSN 1742-6588, 06/2015, Volume 621, Issue 1
J. Phys.: Conf. Ser. 621 (2015), 012011 We find the equivalence groupoid of a~class of $(1+1)$-dimensional second-order evolution equations, which are called... 
Conference Proceeding
The Annals of probability, ISSN 0091-1798, 11/2015, Volume 43, Issue 6, pp. 3359 - 3467
We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In... 
Immigration | Continuous decomposition | Stochastic partial differential equations | Super-Brownian motion | super-Brownian motion | immigration | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | continuous decomposition | UNIQUENESS | Mathematics - Probability | 35R60 | 35K05 | 60H15 | 60J68
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 7/2019, Volume 39, Issue 4, pp. 1185 - 1194
In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the... 
Heat equation | Analysis | heat kernel | 53C44 | Li-Yau-type gradient estimate | Mathematics, general | 35K05 | Mathematics
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 3/2019, Volume 39, Issue 2, pp. 618 - 626
We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes... 
heat equation | optimal | Analysis | general decay | Mathematics, general | 35K05 | Mathematics | viscoelastic
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 4/2018, Volume 24, Issue 1, pp. 203 - 217
In this work we find a sequence of functions $$f_n$$ fn at which the integral 1$$\begin{aligned} v(t,x)=\int _{-\infty }^{\infty }e^{i\lambda x-\lambda... 
Heat equation | 35C99 | Rayleigh-type equation | Mathematics, general | Primary: 30E25 | 35K05 | Mathematics | Secondary: 60H30 | Pearcey function | Boundary crossing
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 08/2018, Volume 63, Issue 7-8, pp. 1142 - 1167
This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far... 
35K05 | Primary: 32D15 | inegral formulas | Secondary: 35J56 | Analytic continuation | Cauchy problem | MATHEMATICS | RIEMANN-HYPOTHESIS | SPACES
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2017, Volume 56, Issue 1, pp. 1 - 8
We show a connection between the $$CDE'$$ C D E ′ inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 2/2011, Volume 183, Issue 2, pp. 245 - 336
In (0,T)×Ω, Ω open subset of ℝ n , n≥2, we consider a parabolic operator P=∂ t −∇ x δ(t,x)∇ x , where the (scalar) coefficient δ(t,x) is piecewise smooth in... 
35K20 | Mathematics, general | 35K05 | Mathematics | 35S15 | MATHEMATICS | EXACT CONTROLLABILITY | DIMENSIONAL HEAT-EQUATION | Projectors | Anisotropy | Analysis of PDEs
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2019, Volume 292, Issue 4, pp. 805 - 825
In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for... 
heat content | 60J75 | infinitesimal generator | Lévy process | 60G51 | spectral heat content | 35K05 | MATHEMATICS | Levy process | SETS | PERIMETER
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 9
We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | RICCI CURVATURE | COMPLEXES | Mathematics - Differential Geometry
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2012, Volume 252, Issue 2, pp. 1403 - 1420
In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations:ut=δF(u), with F (u)>0, on... 
Fast Diffusion Equation | Liouville-type theorem | 35K05 | Porous Media Equation | 53C21 | Localized Hamilton-type gradient estimate
Journal Article
Journal Article
Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 24
Journal Article
Numerische Mathematik, ISSN 0029-599X, 6/2018, Volume 139, Issue 2, pp. 315 - 348
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 6/2014, Volume 14, Issue 2, pp. 477 - 497
For a finite not necessarily compact metric graph, one considers the differential expression $${-\frac{d^2}{d x^2}}$$ - d 2 d x 2 on each edge. The boundary... 
47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED
Journal Article
The Annals of probability, ISSN 0091-1798, 09/2014, Volume 42, Issue 5, pp. 2032 - 2112
Motivated by Girsanov’s nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE)... 
35K05 | white noise | 35R60 | Heat equation | 60H15 | stochastic partial differential equations
Journal Article
Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 06/2020, Volume 28, Issue 3, pp. 349 - 366
A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for... 
80A23 | heat equation | 35R30 | wave equation | 35L05 | 35K05 | 35J05 | cavity | non-destructive testing | 74J25 | inclusion | 74F05 | 35Q79 | Enclosure method | 35B40 | inverse obstacle problem | displacement-temperature equation of motion | 35R05 | Thermodynamics | Temperature distribution | Boundary value problems | Elastic waves | Inclusions | Heat flux
Journal Article
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