Multiple blowup of solutions for a semilinear heat equation II
Keywords: 35K20; 35K55; 58K57Semilinear heat equation; Supercritical; Incomplete blowup; Multiple blowup
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Solutions of the anisotropic porous medium equation in RnRn under an L1L1-initial value
Keywords: 35K55; 35K65Anisotropic diffusion; Degenerate parabolic equation; Comparison principle; Large time behavior
Boundedness of global solutions of a porous medium equation with a localized source
Keywords: 35K55; 35K65; 35A07; 35B35Porous medium equation; Localized source; Global existence; Finite time blow-up; Uniform boundedness
The compact support property for measure-valued processes
Keywords: primary; 60J60; 60J80; secondary; 35K15; 35K55; Semilinear equation; Elliptic equation; Positive solutions; Uniqueness of the Cauchy problem; Compact support property; Superprocess; Superdiffusion; Super-Brownian motion; Measure-valued process; h-transfor
Growup of solutions for a semilinear heat equation with supercritical nonlinearity
Keywords: 35K20; 35K55; 58K57Semilinear heat equation; Supercritical; Growup
Existence of solutions to initial value problem for a parabolic Monge-Ampère equation and application
Keywords: 35k55; 35k15; 91b26; Parabolic Monge-Ampère equation; Initial value problem; Unbounded initial function; Optimal portfolio;
Weak Dirichlet processes with a stochastic control perspective
Keywords: 60G05; 60G44; 60G48; 60H05; 60H10; 60J60; 35K15; 35K55; 35J15; 93E20Stochastic calculus via regularization; Weak Dirichlet processes; Stochastic optimal control; Cauchy problem for parabolic partial differential equations
A geometrical similarity between migration of human population and diffusion of biological particles
Keywords: 35K55; 45K05; 92D25; 91D25Nonlinear diffusion; Migration of human population; Fokker–Planck equation; Master equation; Quasilinear partial differential equation of parabolic type; Nonlinear integro-partial differential equation
Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
Keywords: 35K55; 35K65; 35B45; 35K20Nonlinear parabolic problems; Gradient term with quadratic growth; Existence and regularity; Bounded and unbounded solutions; Lack of coerciveness
Weak existence and uniqueness for forward–backward SDEs
Keywords: primary; 65C30; secondary; 35K55; 60H10; 60H30FBSDEs; Gradient estimates; Quasi-linear PDEs; Calderón and Zygmund estimates; Schauder’s estimates; Weak existence and uniqueness
Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method
Keywords: 35-04; 35K55; 37K05; 65M06Finite difference; The discrete variational derivative method; Partial differential equation with variable coefficients; Energy dissipation
Nonexistence of solutions to Hele-Shaw equations
Keywords: primary 35J85; 35D05; secondary 35R35; 35B45; 35J65; 35K55; 76D27; p-Laplace operator; Hele-Shaw flows; Pohozaev identity;
On global existence for semilinear parabolic systems
Keywords: 35K55; Parabolic systems; Global solutions;
Renormalization and scaling methods for quasi-static interface problems
Keywords: 82C24; 82B24; 35K55; Renormalization group; Scaling; Interface dynamics; Quasi-static regime; Capillarity length;
Spatial decay bounds for a class of quasi-linear parabolic initial-boundary value problems
Keywords: 35K55; 35K60; 35B50; Quasi-linear parabolic problems; Non-linear heat conduction; Saint-Venant principle; Maximum principles;
A compactness theorem of n-harmonic maps
Keywords: 35K55; 58J35; Harmonic maps; Coulomb gauge frame; Compensated-compactness;
Nonlinear degenerate parabolic equations with measure data
Keywords: 35K65; 35K55; Nonlinear degenerate parabolic equations; Existence; Measure data;
Various behaviors of solutions for a semilinear heat equation after blowup
Keywords: 35K20; 35K55; 58K57; Incomplete blowup; Peaking solution; Semilinear heat equation;
On the Kneser property for some parabolic problems
Keywords: 35B40; 35B41; 35K55; 35K57; 37B25; 58C06; Phase-field equations; Differential inclusions; Setvalued dynamical system; Global attractor; Connexion; Kneser property;
Spreading speeds as slowest wave speeds for cooperative systems
Keywords: 92D40; 92D25; 35K55; 35K57; Traveling waves; Cooperative systems; Spreading speed; Reaction-diffusion; Discrete-time systems;
Homogenization for fully nonlinear parabolic equations
Keywords: 49L25; 35B27; 35K55; Homogenization; Viscosity solutions; Nonlinear parabolic equations;
Phase change problems with temperature dependent constraints for the volume fraction velocities
Keywords: 35K45; 35K55; 35K90; Phase change problems; Doubly nonlinear evolution equation; Schauder's fixed point theory; Subdifferential operator;
On a Cahn-Hilliard model for phase separation with elastic misfit
Keywords: 35K35; 35K55; 35J50; 73C02; 35B65; 35J45; 82C26; Cahn-Hilliard systems; Elasticity; Regularity; Elliptic-parabolic systems; Phase transition;
A finite element method for surface diffusion: the parametric case
Keywords: 35K55; 65M12; 65M15; 65M60; 65Z05; Surface diffusion; Fourth-order parabolic problem; Finite elements; Schur complement; Smoothing effect; Pinch-off;
Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets
Keywords: 35K60; 35K55; 35Q80; Quasilinear equation; Quadratic gradient; Existence and uniqueness of solutions; Incomplete financial markets;
Nonlinear optimal control problems of degenerate parabolic equations with logistic time-varying delays of convolution type
Keywords: 49J20; 49J50; 49K25; 35K65; 35K55; 35B50; Optimal control; Degenerate parabolic equations; Logistic growth; Time-varying delays; Convolution type; Viscosity solution; Necessary conditions; Population dynamics;
A non-local regularization of first order Hamilton-Jacobi equations
Keywords: 35B65; 35B05; 35G25; 35K55; Integro-differential Hamilton-Jacobi equation; Non-local regularization; Lévy operator; Viscosity solution; Error estimate;
Two-dimensional travelling wave solutions of a system modelling near equidiffusional flames
Keywords: 35J55; 35J60; 35K55; 80A25; Combustion; Elliptic systems; Travelling waves; Unbounded domains;
Asymptotics of the porous media equation via Sobolev inequalities
Keywords: 58J35; 47J35; 35K55; Porous mdeia equation; Logarithmic Sobler inequalities; Asymptotics;
A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
Keywords: 35K55; 35K65; 35B05; 35B30; Nonlinear parabolic equations; Nonstandard growth conditions;
Blow-up results for a class of first-order nonlinear evolution inequalities
Keywords: 35K55; 35R45; Blow-up; Nonlinear inhomogeneous parabolic inequalities; Test function method;
The Cauchy problem for ut=Îu+|âu|q, large-time behaviour
Keywords: 35K55; Surface growth; KPZ equation; Viscous Hamilton-Jacobi equation; Nonlinear second-order parabolic; Temporal decay estimate; Large-time behaviour;
The existence and stability of travelling waves with transition layers for some singular cross-diffusion systems
Keywords: 35B25; 35B35; 35K45; 35K55; 47A75; Existence; Stability; Travelling waves; Cross-diffusion system; Spectral analysis; Unstable bundle;
The multi-dimensional super-replication problem under gamma constraints
Keywords: 91B28; 35K55; 60H30; Gamma constraints; Super-replication; Viscosity solutions; Parabolic majorant; Double stochastic integrals; Contrainte gamma; Sur-réplication; Solutions de viscosité; Majorant parabolique; Intégrales stochastiques doubles;
Large time behavior for a viscous Hamilton-Jacobi equation with Neumann boundary condition
Keywords: 35K55; 35K60; 35B33; 35B35; 35B65; Nonlinear parabolic equation; Viscous Hamilton-Jacobi equation; Neumann boundary condition; Large time behaviour; Bernstein technique;
Second order parabolic systems, optimal regularity, and singular sets of solutions
Keywords: Partial regularity; Parabolic systems; Singular sets; 35K55; 35D10;
The instability of spiky steady states for a competing species model with cross diffusion
Keywords: 35B25; 35B35; 35K20; 35K55; 35K57; Cross-diffusion systems; Spiky steady states; Instability; Spectral analysis;
The heat flow in nonlinear Hodge theory
Keywords: 58A14; 58J35; 35J50; 35J60; 35K45; 35K55; 53C44; 76N10; Ï-Harmonic exterior forms; Nonlinear Hodge theory; Heat flow method; Exterior curvature operator; Mean curvature flow; Gas dynamics;