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$L^1$estimates for the higherorder derivatives of solutions to parabolic equations subject to initial values of bounded total variation
1.  Sobolev Institute of Mathematics, 4, Acad. Koptyug prosp., 630090 Novosibirsk, Russian Federation 
2.  Dipartimento di Matematica, Università “Roma Tre”, 1, Largo S. L. Murialdo, 00146 Rome, Italy 
[1] 
Yohei Fujishima. On the effect of higher order derivatives of initial data on the blowup set for a semilinear heat equation. Communications on Pure & Applied Analysis, 2018, 17 (2) : 449475. doi: 10.3934/cpaa.2018025 
[2] 
Francis Ribaud. Semilinear parabolic equations with distributions as initial data. Discrete & Continuous Dynamical Systems  A, 1997, 3 (3) : 305316. doi: 10.3934/dcds.1997.3.305 
[3] 
Lucas C. F. Ferreira, Elder J. VillamizarRoa. On the heat equation with concaveconvex nonlinearity and initial data in weak$L^p$ spaces. Communications on Pure & Applied Analysis, 2011, 10 (6) : 17151732. doi: 10.3934/cpaa.2011.10.1715 
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Joana Terra, Noemi Wolanski. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data. Discrete & Continuous Dynamical Systems  A, 2011, 31 (2) : 581605. doi: 10.3934/dcds.2011.31.581 
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Yohei Fujishima. Blowup set for a superlinear heat equation and pointedness of the initial data. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 46174645. doi: 10.3934/dcds.2014.34.4617 
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Luz de Teresa, Enrique Zuazua. Identification of the class of initial data for the insensitizing control of the heat equation. Communications on Pure & Applied Analysis, 2009, 8 (1) : 457471. doi: 10.3934/cpaa.2009.8.457 
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Yaobin Ou, Pan Shi. Global classical solutions to the free boundary problem of planar full magnetohydrodynamic equations with large initial data. Discrete & Continuous Dynamical Systems  B, 2017, 22 (2) : 537567. doi: 10.3934/dcdsb.2017026 
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Bingkang Huang, Lan Zhang. A global existence of classical solutions to the twodimensional VlasovFokkerPlanck and magnetohydrodynamics equations with large initial data. Kinetic & Related Models, 2019, 12 (2) : 357396. doi: 10.3934/krm.2019016 
[9] 
ZhiQiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initialboundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure & Applied Analysis, 2015, 14 (3) : 759792. doi: 10.3934/cpaa.2015.14.759 
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Kazuhiro Ishige. On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data. Discrete & Continuous Dynamical Systems  A, 1995, 1 (4) : 521546. doi: 10.3934/dcds.1995.1.521 
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Fengbai Li, Feng Rong. Decay of solutions to fractal parabolic conservation laws with large initial data. Communications on Pure & Applied Analysis, 2013, 12 (2) : 973984. doi: 10.3934/cpaa.2013.12.973 
[12] 
Brian Smith and Gilbert Weinstein. On the connectedness of the space of initial data for the Einstein equations. Electronic Research Announcements, 2000, 6: 5263. 
[13] 
SeungYeal Ha, Bingkang Huang, Qinghua Xiao, Xiongtao Zhang. A global existence of classical solutions to the twodimensional kineticfluid model for flocking with large initial data. Communications on Pure & Applied Analysis, 2020, 19 (2) : 835882. doi: 10.3934/cpaa.2020039 
[14] 
YoungSam Kwon, Antonin Novotny. Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data. Discrete & Continuous Dynamical Systems  A, 2020, 40 (1) : 395421. doi: 10.3934/dcds.2020015 
[15] 
Justin Forlano. Almost sure global well posedness for the BBM equation with infinite $ L^{2} $ initial data. Discrete & Continuous Dynamical Systems  A, 2020, 40 (1) : 267318. doi: 10.3934/dcds.2020011 
[16] 
Rosaria Di Nardo. Nonlinear parabolic equations with a lower order term and $L^1$ data. Communications on Pure & Applied Analysis, 2010, 9 (4) : 929942. doi: 10.3934/cpaa.2010.9.929 
[17] 
Manil T. Mohan, Sivaguru S. Sritharan. $\mathbb{L}^p$solutions of the stochastic NavierStokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data. Evolution Equations & Control Theory, 2017, 6 (3) : 409425. doi: 10.3934/eect.2017021 
[18] 
Eduardo Casas, Boris Vexler, Enrique Zuazua. Sparse initial data identification for parabolic PDE and its finite element approximations. Mathematical Control & Related Fields, 2015, 5 (3) : 377399. doi: 10.3934/mcrf.2015.5.377 
[19] 
Joel Avrin. Global existence and regularity for the Lagrangian averaged NavierStokes equations with initial data in $H^{1//2}$. Communications on Pure & Applied Analysis, 2004, 3 (3) : 353366. doi: 10.3934/cpaa.2004.3.353 
[20] 
Dongming Wei. 1D VlasovPoisson equations with electron sheet initial data. Kinetic & Related Models, 2010, 3 (4) : 729754. doi: 10.3934/krm.2010.3.729 
2018 Impact Factor: 0.925
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