Initial-boundary value problems for conservative Kimura-type equations: solvability, asymptotic and conservation law

[1]  James Michael MacFarlane,et al.  Existence , 2014, Encyclopedia of African Religions and Philosophy.

[2]  Camilla Nobili,et al.  Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spaces , 2020, Journal of Evolution Equations.

[3]  Linan Chen,et al.  Fundamental Solution to 1D Degenerate Diffusion Equation with Locally Bounded Coefficients , 2020, Journal of Mathematical Analysis and Applications.

[4]  F. Punzo,et al.  Distance from submanifolds with boundary and applications to Poincaré inequalities and to elliptic and parabolic problems , 2019, Journal of Differential Equations.

[5]  F. Punzo.  Integral conditions for uniqueness of solutions to degenerate parabolic equations , 2019, Journal of Differential Equations.

[6]  C. Epstein,et al.  The Feynman–Kac formula and Harnack inequality for degenerate diffusions , 2017 .

[7]  C. Epstein,et al.  Transition probabilities for degenerate diffusions arising in population genetics , 2016, 1608.02119.

[8]  C. Epstein,et al.  Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology , 2014, 1406.1426.

[9]  C. Pop.  $C^0$-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators , 2014, 1406.0742.

[10]  C. Pop.  Existence, uniqueness and the strong Markov property of solutions to Kimura diffusions with singular drift , 2014, 1406.0745.

[11]  Max O. Souza,et al.  Discrete and continuous SIS epidemic models: A unifying approach , 2014 .

[12]  F. Punzo.  Uniqueness of solutions to degenerate parabolic and elliptic equations in weighted Lebesgue spaces , 2013 .

[13]  P. Feehan,et al.  On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Ito processes , 2012, 1211.4636.

[14]  P. Feehan,et al.  A SCHAUDER APPROACH TO DEGENERATE-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED COEFFICIENTS , 2011, 1112.4824.

[15]  P. Feehan,et al.  Boundary-degenerate elliptic operators and Holder continuity for solutions to variational equations and inequalities , 2011, 1110.5594.

[16]  C. Epstein,et al.  Degenerate Diffusion Operators Arising in Population Biology , 2011, 1110.0032.

[17]  F. A. Chalub,et al.  The frequency-dependent Wright–Fisher model: diffusive and non-diffusive approximations , 2011, Journal of mathematical biology.

[18]  M. Pozio,et al.  Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients , 2011 .

[19]  Max O. Souza,et al.  The SIR epidemic model from a PDE point of view , 2009, Math. Comput. Model..

[20]  K. S. Kumar.  A class of degenerate stochastic differential equations with non-Lipschitz coefficients , 2009, 0904.2629.

[21]  Fabio A C C Chalub,et al.  From discrete to continuous evolution models: A unifying approach to drift-diffusion and replicator dynamics. , 2008, Theoretical population biology.

[22]  M. Pozio,et al.  Criteria for well-posedness of degenerate elliptic and parabolic problems , 2008 .

[23]  F. A. Chalub,et al.  A non-standard evolution problem arising in population genetics , 2008, 0801.1335.

[24]  B. Bazalii,et al.  On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain , 2007 .

[25]  M. Pozio,et al.  On the uniqueness of bounded solutions to singular parabolic problems , 2005 .

[26]  A. Cherny,et al.  Singular Stochastic Differential Equations , 2004 .

[27]  S. Cerrai,et al.  Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations , 2004 .

[28]  R. Bass,et al.  Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains , 2002 .

[29]  R. Bass,et al.  Degenerate stochastic differential equations and super-Markov chains , 2002 .

[30]  B. Bazalii,et al.  On the Solvability of the Hele–Shaw Model Problem in Weighted Hölder Spaces in a Plane Angle , 2000 .

[31]  D. Dawson,et al.  Resolvent Estimates for Fleming-Viot Operators and Uniqueness of Solutions to Related Martingale Problems , 1995 .

[32]  O. A. Ladyzhenskai︠a︡,et al.  Linear and Quasi-linear Equations of Parabolic Type , 1995 .

[33]  S. Ethier.  A class of degenerate diffusion processes occurring in population genetics , 1976 .

[34]  Paul C. Fife,et al.  Second-Order Equations With Nonnegative Characteristic Form , 1973 .

[35]  S. Varadhan,et al.  On degenerate elliptic‐parabolic operators of second order and their associated diffusions , 1972 .

[36]  D. Aronson.  Uniqueness of solutions of the Cauchy problem for parabolic equations*1 , 1966 .

[37]  C. Epstein,et al.  The Geometric Microlocal Analysis of Generalized Kimura and Heston Diffusions , 2014 .

[38]  A. Cherny.  On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations , 2002 .

[39]  O. Ladyzenskaya.  On the linear and quasilinear parabolic equations , 1967 .