Publication Information

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'Polynomial': [56, 117, 153, 386, 420], 'Trigonometric': [59, 179, 393], 'Exponential': [62, 181], 'Remarks': [64, 130, 208, 279, 328, 399, 453, 504, 552], 'Comments': [66, 132, 210, 281, 330, 401, 455, 506, 554], 'the': [68, 134, 194, 212, 283, 332, 357, 403, 447, 457, 477, 485, 493, 508, 529, 556], 'Literature': [69, 135, 213, 284, 333, 404, 458, 509, 557], 'MODULES:': [73], 'MATHEMATICS': [74], 'ONE': [76, 141, 293], 'DIMENSION': [77], 'Main': [78], 'Theorem': [79], 'The': [83, 205], 'Optimal': [84], 'Estimate': [85], 'Dimension': [87, 97, 104], 'First-Order': [91, 501], 'Operators': [92, 99, 109, 115, 122, 186, 345, 355, 365, 369, 376, 421, 527, 539, 545], 'with': [93, 100, 110, 166], 'Maximal': [96, 103], 'Second-Order': [98, 107, 344, 354, 363], 'First-': [105], 'Quadratic': [108, 177, 240, 422], 'Lower': [113], 'Dimensions': [114], 'Preserving': [116], '?/?t-Dependent': [121], 'Summary:': [123], 'Types': [125], 'Equations': [127, 163, 176, 188, 233, 247, 257, 265, 267, 278, 303, 311, 327, 383, 424, 442], 'Open': [136, 214, 285, 334, 405, 459, 558], 'Problems': [137, 215, 286, 335, 406, 460, 559], 'PARABOLIC': [138, 464], 'DIMENSION:': [142, 294], 'THIN': [143], 'FILM,': [144], 'KURAMOTO-SIVASHINSKY,': [145], 'MAGMA': [147], 'Thin': [149, 174, 184, 374], 'Film': [150, 175, 185, 375], 'Models': [151, 201, 243, 314], 'Applications': [155, 547, 548], 'Extinction,': [157], 'Blow-Up,': [158], 'Free-Boundary': [159], 'Problems,': [160], 'Interface': [162, 246, 317], 'Zero': [167], 'Contact': [168], 'Angle': [169], 'Extinction': [170], 'Behavior': [171, 192], 'for': [172, 231, 254, 262, 275, 353, 368, 419, 440, 446, 525, 537], 'Sixth-Order': [173], 'Models:': [178, 204], '2mth-Order': [183], 'Oscillatory,': [189], 'Changing': [190], 'Sign': [191], 'in': [193, 199, 238, 260, 300, 308, 322, 360, 380, 388, 395, 451], 'Cauchy': [195], 'Problem': [196, 521, 531], 'Kuramoto-Sivashinsky-Type': [200], 'Quasilinear': [202, 309, 469], 'Pseudo-Parabolic': [203], 'Magma': [206], 'Equation': [207, 450], 'ODD-ORDER': [216], 'ONE-DIMENSIONAL': [217], 'KORTEWEG-DE': [219], 'VRIES,': [220], 'COMPACTON,': [221], 'DISPERSION,': [223], 'HARRY': [225], 'DYM': [226], 'Blow-Up': [228, 299, 313], 'Localization': [230], 'KdV-Type': [232], 'Compactons': [234, 251, 259, 319], 'Shocks': [236], 'Waves': [237], 'Higher-Order': [239, 244, 348, 373, 441], 'Nonlinear': [241, 263, 301, 325, 381], 'Dispersion': [242, 264, 382], 'PDEs:': [245], 'Oscillatory': [249, 273], 'Interfaces': [253], 'Singular': [255], 'mKdV-Type': [256], 'On': [258, 356, 362, 528], 'IRN': [261, 343, 452], 'Tautological': [266], 'Peakons': [269], 'Subspaces,': [270], 'Singularities,': [271], 'Harry': [276], 'Dym-Type': [277], 'WAVE': [288], 'BOUSSINESQ': [290], 'SYSTEMS': [295], 'OF': [296, 415, 562], 'Wave': [302, 310], 'Breathers': [307], 'Quenching': [315], 'Phenomena,': [318], 'Systems': [323], 'Evolution': [326], 'APPLICATIONS': [336], 'TO': [337], 'Some': [347], 'Extended': [350], 'Remarkable': [358], 'Operator': [359], 'IR2': [361], 'p-Laplacian': [364], 'Monge-Ampere': [371], 'Type': [372], 'Moving': [377, 543], 'Compact': [378], 'Structures': [379], 'From': [384], 'IR': [389, 396], 'N': [390, 397], '-1': [398], 'PARTIALLY': [407], 'SUBSPACES,': [409], 'SETS,': [411], 'GENERALIZED': [413], 'SEPARATION': [414], 'VARIABLES': [416], 'Partial': [417], 'Invariance': [418], 'Kuramoto-Sivashinsky': [423], 'Method': [425], 'Partially': [434], 'Modules': [436], 'Evolutionary': [437], 'Sets': [439], 'A': [443], 'Technique': [445], 'Porous': [448], 'Medium': [449], 'SIGN-INVARIANTS': [461], 'FOR': [462, 512], 'SECOND-ORDER': [463], 'Definitions,': [471], 'Examples': [474], 'Sign-Invariants': [475, 483, 491, 503], 'Form': [478, 486, 494], 'ut': [479, 495], '-': [480, 496, 498], '?(u)': [481], 'Stationary': [482], 'H': [487], '(r,': [488], 'u,': [489], 'ur)': [490], 'm(u)(ux)2': [497], 'M(u)': [499], 'General': [500], 'Hamilton-Jacobi': [502], 'DISCRETE': [513], 'OPERATORS,': [514], 'MOVING': [515], 'MESH': [516], 'METHODS,': [517], 'LATTICES': [519], 'Backward': [520], 'Discrete': [526], 'Forward': [530], 'Finite-Difference': [538], 'Properties': [541], 'Mesh': [544], 'Anharmonic': [550], 'Lattices': [551], 'REFERENCES': [560], 'LIST': [561], 'FREQUENTLY': [563], 'USED': [564], 'ABBREVIATIONS': [565], 'INDEX': [566]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W30786189', 'counts_by_year': [{'year': 2024, 'cited_by_count': 23}, {'year': 2023, 'cited_by_count': 24}, {'year': 2022, 'cited_by_count': 20}, {'year': 2021, 'cited_by_count': 23}, {'year': 2020, 'cited_by_count': 26}, {'year': 2019, 'cited_by_count': 31}, {'year': 2018, 'cited_by_count': 42}, {'year': 2017, 'cited_by_count': 22}, {'year': 2016, 'cited_by_count': 14}, {'year': 2015, 'cited_by_count': 17}, {'year': 2014, 'cited_by_count': 19}, {'year': 2013, 'cited_by_count': 23}, {'year': 2012, 'cited_by_count': 13}], 'updated_date': '2025-01-09T09:22:17.007197', 'created_date': '2016-06-24'}